UC-NRLF 


24    314 


FLAMES 


AND  O 


INCANDESCENT   SOLIDS 


LSON, 


THE    ELECTRICAL    PROPERTIES 
OF    FLAMES   AND   OF    INCANDESCENT 

SOLIDS 


THE 

ELECTRICAL  PROPERTIES 
OF    FLAMES 

AND   OF 

INCANDESCENT   SOLIDS 


BY 

HAROLD    A.    WILSON 

M 

D.SC.  (LONDON),  M.A.,  F.R.S.,  F.R.S.C. 

FORMERLY  FELLOW  OF  TRINITY  COLLEGE,  CAMBRIDGE,  AND  PROFESSOR  OF 

PHYSICS  IN  KING'S  COLLEGE,  UNIVERSITY  OF  LONDON,  MACDONALD 

PROFESSOR  OF  PHYSICS  IN  MCGILL  UNIVERSITY,  MONTREAL 


Xonbon :  IQnfteraitg  of  Xonbon  pre06 

PUBLISHED  FOR  THE  UNIVERSITY  OF  LONDON  PRESS,  LTD. 
BY   HODDER  &   STOUGHTON,    WARWICK   SQUARE,  E.C. 

1912 


HODDER   AND    STOUGHTON 

PUBLISHERS  TO 


THE   UNIVERSITY   OF   LONDON   PRESS 


ur. 


PREFACE 

THIS  book  is  intended  to  give  a  concise  but  fairly 
complete  account  of  recent  researches  on  the  electrical 
properties  of  incandescent  bodies  and  of  flames.  I  have 
attempted  to  present  the  mathematical  theory  required  in 
as  simple  a  form  as  possible,  without  loss  of  accuracy,  and 
to  make  estimates  of  the  reliability  of  some  of  the  measure- 
ments described.  Some  matter  not  hitherto  published  is 
contained  in  the  book. 

H.  A.  W. 

January  1912. 


CONTENTS 

/ 

CHAP.  PAGE 

I     INTRODUCTION 1 

II     THE    DISCHARGE    OF    NEGATIVE    ELECTRICITY    BY   HOT 

PLATINUM  IN  A  VACUUM      ......         4 

III     THE    DISCHARGE    OF    NEGATIVE    ELECTRICITY    BY    HOT 

PLATINUM  IN  HYDROGEN  AND  OTHER  GASES          .         .       16 

IV     THE  DISCHARGE  OF  NEGATIVE  ELECTRICITY  BY  VARIOUS 

SUBSTANCES 28 

V     THE  DISCHARGE  OF  POSITIVE  ELECTRICITY  BY  HOT  BODIES       33 

VI     THE  CONDUCTIVITY  OF  THE  BUNS  EN  FLAME    .         .         .57 

VII     THE  ELECTRICAL  CONDUCTIVITY  OF  SALT  VAPOURS          .       70 

VIII     THE  ELECTRICAL  CONDUCTIVITY  OF  FLAMES  FOR  RAPIDLY 

ALTERNATING  CURRENTS 100 

IX     FLAMES  IN  A  MAGNETIC  FIELD  112 


ELECTRICAL  PROPERTIES 
OF  FLAMES 


CHAPTER   I 
INTRODUCTION 

THAT  flames  conduct  electricity  and  that  hot  bodies  lose  an 
electrical  charge  and  various  other  associated  facts  have  been 
known  for  more  than  a  century,  but  it  is  only  during  the  last 
twenty  years  that  the  electrical  properties  of  bodies  at  high 
temperatures  have  been  systematically  investigated. 

The  earlier  observations  are  mostly  of  a  purely  qualitative 
character,  and  the  conditions  of  the  experiments  described  not 
sufficiently  definite  for  them  to  be  of  much  use  for  an  accurate 
comparison  between  theory  and  experiment. 

The  development  of  the  ionic  theory  of  the  electrical  pro- 
perties of  gases  by  Sir  J.  J.  Thomson  led  to  numerous  experi- 
mental investigations,  which  naturally  included  an  examination 
of  the  electrical  properties  of  flames  and  hot  solids  in  the  light 
of  the  new  theory.  In  consequence  a  great  increase  in  our 
knowledge  of  the  relations  between  matter  and  electricity  at 
high  temperatures  has  taken  place  and  the  ionic  theory  has 
become  firmly  established  in  this  field. 

The  following  pages  contain  an  account  of  many  of  the  more 
recent  investigations  on  the  electrical  properties  of  hot  bodies 
and  flames,  especially  of  such  as  are  of  a  quantitative  character 
giving  results  capable  of  accurate  comparison  with  theory. 

Elster  and  Geitel l  made  a  great  many  observations  on  the 
charge  acquired  by  an  insulated  plate  put  near  hot  wires  in 
different  gases  at  various  pressures. 

1  Wied.  Ann.  1882,  1883,  1884,  1885,  1887,  1889. 

B  1 


2  ELECTRICAL  PROPERTIES   OF   FLAMES 

Sir  J.  J.  Thomson  l  measured  the  conductivity  of  many  gases 
and  vapours  of  salts  and  metals  between  platinum  electrodes 
at  a  bright  red  heat.  Gases  and  vapours  which  dissociate  he 
found  conduct  very  much  better  than  those  which  do  not. 

Sir  J.  J.  Thomson2  in  1899  determined  the  ratio  of  the  charge 
e  to  the  mass  m  of  the  negative  ions  emitted  by  an  incandescent 
carbon  filament  in  hydrogen  at  a  low  pressure,  and  found  it  equal 
to  about  107,  which  is  the  value  of  e/m  for  electrons. 

McClelland 3  examined  gases  which  had  been  drawn  past  a 
hot  platinum  wire  and  showed  that  they  contained  positive  and 
negative  ions.  The  velocity  of  these  ions  due  to  an  electric 
field  he  found  was  very  small  and  smaller  the  hotter  the  wire. 

The  writer4  examined  the  variation  of  the  current  from 
hot  platinum  in  air  with  the  temperature,  and  from  the  rate 
of  variation  calculated  the  energy  rendered  latent  by  the 
formation  of  the  ions  at  the  surface  of  the  platinum. 

Rutherford 5  measured  the  velocity  of  the  ions  emitted  by 
hot  platinum  in  air  and  found  that  the  ions  had  a  considerable 
range  of  velocities.  The  average  velocity  increased  with  the 
temperature. 

O.  W.  Richardson6  examined  the  current  from  hot  platinum 
in  a  vacuum  and  explained  its  variation  with  the  temperature  by 
supposing  that  the  electrons  in  the  metal,  to  which  its  conduc- 
tivity is  due,  escape  at  high  temperatures.  Richardson's  theory 
is  now  well  established  as  the  result  of  many  investigations  by 
himself  and  others. 

Giese7  investigated  the  electrical  properties  of  the  gases 
coming  from  flames  and  explained  many  of  them  on  the  ionic 
theory. 

McClelland8  determined  the  velocities  of  the  ions  in  gases 
drawn  from  flames  and  found  them  to  vary  from  0'23  cm.  per 

1  Phil.  Mag.  V.  29,  pp.  358,  441,  1890. 

2  Phil.  Mag.  V.  48,  p.  547, 1899.     • 

3  Proc.  Camb.  Phil.  tioc.  vol.  x.  p.  241,  1900. 

4  Phil.  Trans.  A.  vol.  197,  p.  415,  1901. 

5  Physical  Review,  vol.  xiii.,  December  1901. 

6  Proc.  Camb.  Phil.  Soc.  vol.  xL  p.  286,  1902. 

7  Wied.  Ann.  vol.  xvii.  pp.  1,  236,  519,  1882  ;  vol.  xxxviii.  p.  403,  1889. 
^  8  Phil.  Mag.  V.  46,  p.  29,  1898. 


INTRODUCTION  3 

sec.  for   one  volt  per  cm.  near  the  flame  to  0'04  cm.  per  sec. 
some  distance  away. 

Arrhenius  l  in  1891  investigated  the  conductivity  of  flames 
containing  salt  vapours,  and  found  that  the  conductivity  due  to 
salts  of  the  alkali  metals  increases  rapidly  with  the  atomic  weight 
of  the  metal. 

Arrhenius'  results  were  confirmed  and  extended  by  Smithells, 
Dawson,  and  the  writer.2 

The  writer 3  measured  the  velocity  of  the  ions  in  flames,  and 
showed  later4  that  Faraday's  laws  of  electrolysis  apply  to  alkali 
salt  vapours  at  high  temperatures. 

The  investigations  just  mentioned  are  some  of  the  first  of 
those  in  which  definite  quantities  were  measured.  Most  of  the 
above  and  subsequent  researches  are  described  more  fully  in 
the  following  chapters. 

A  full  account  of  the  old  experiments  is  given  in  Wiede- 
mann's  Eleldricitat,  Bd.  IV.  B.  Sir  J.  J.  Thomson,  in  Conduction  of 
Mcdridty  through  Gases,  gives  a  summary  of  the  most  important 
observations  made  by  the  earlier  experimenters  and  references  to 
their  papers. 

I  have  not  discussed  the  numerous  observations  which  have 
been  made  on  gases  drawn  from  flames  or  from  the  neighbour- 
hood of  hot  wires.  These  observations  show  that  ions  are 
present  in  such  gases  and  their  velocities  have  been  found. 
Also  I  have  not  given  any  account  of  the  numerous  observa- 
tions on  the'  deflection  of  flames  by  electric  and  magnetic  fields. 

1  Wied.  Ann.  vol.  xliii.  p.  18,  1891. 

2  Phil  Trans.  A.  vol.  193,  p.  89,  1899.'' 

3  Phil.  Trans.  A.  vol.  192,  p.  499,  1899. 

4  Phil.  Trans.  A.  vol.  197,  p.  415,  1901.  ^ 


B  2 


CHAPTER   II 


THE  DISCHARGE  OF  NEGATIVE  ELECTRICITY  BY 
HOT   PLATINUM  IN  A  VACUUM 

WHEN  a  negatively  charged  clean  wire  of  pure  platinum  is 
raised  to  a  high  temperature  in  a  vacuum,  it  is  found  to  lose  its 
charge.  If  the  negative  terminal  of  a  battery  is  connected  to  the 
hot  wire,  and  the  positive  terminal  to  a  conductor  near  the  wire, 
a  continuous  current  passes  between  the  con- 
ductor and  the  wire  through  the  vacuum,  but  if 
the  connections  of  the  battery  are  reversed  little 
or  no  current  is  obtained.  The  current  is  only 
obtained  when  the  wire  is  hot,  so  that  it  is  clear 
that  it  consists  of  negative  electricity  emitted  by 
the  wire.  The  current  obtained  is  about  10 ~n  to 
10  ~7  of  an  ampere  per  sq.  cm.  of  platinum  surface, 
at  a  temperature  of  about  1600°  C.  Much  larger 
currents  than  this  may  be  obtained  if  impurities, 
such  as  hydrogen  and  alkali  metal  salts,  are 
present  in  the  platinum,  even  in  minute  quanti- 
ties. The  current  increases  rapidly  with  the 
temperature  of  the  wire. 

The  above  statements  can  be  verified  with 
the  apparatus  shown  in  Fig.  1.  A  loop  of  pure 
platinum  wire  PP  is  suspended  inside  a  glass 
tube  about  2  cms.  in  diameter  and  12  cms.  long. 
The  ends  of  the  loop  are  attached  to  two  stout 

platinum  wires  DE  sealed  through 

the   upper   end    of  the   tube.      A 
•  cylinder  of  platinum  foil  AB  sur- 
rounds the  loop  and  is  connected  to 
wires  sealed  through  the  lower  end 
of  the  tube  at  F.    A  side  tube  leads 
FIG.  1. 


DISCHARGE   OF  NEGATIVE   ELECTRICITY         5 

to  a  mercury  pump  capable  of  reducing  the  pressure  below  O'OOl 
mm.  of  mercury.  The  loop  may  be  of  wire  0'2  mm.,  and  the 
wires  DE  about  1  mm.  in  diameter.  Before  sealing  the  side 
tube  to  the  pump,  the  apparatus  is  washed  with  boiling  nitric  acid 
and  distilled  water. 

The  loop  is  heated  by  passing  a  current  through  it,  and  its 
resistance  is  found  by  making  it  one  of  the  arms  of  a  Wheatstone's 
bridge.  The  temperature  of  the  loop  is  obtained  from  its  resist- 
ance. The  current  between  the  loop  and  the  cylinder  is  measured 
with  a  galvanometer.  To  get  rid  of  gases  evolved  by  the  apparatus 
when  the  wire  is  heated,  it  is  best  to  admit  air  to  atmospheric 
pressure  and  pump  it  out  several  times  while  the  wire  is  kept  at 
about  1600°  C.  If  these  precautions  are  taken  and  a  good  vacuum 
obtained,  the  current  from  the  wire  will  be  found  to  be  of  the 
order  of  magnitude  stated,  and  will  remain  fairly  constant.  The 
use  of  charcoal  and  liquid  air  greatly  facilitates  the  obtaining  of  a 
good  vacuum. 

According  to  the  ionic  theory,  we  should  expect  the  negative 
electricity  emitted  by  the  wire  to  be  carried  by  charged  atoms,  or 
to  consist  simply  of  free  electrons.  The  ratio  of  the  charge  (e)  to 
the  mass  (in)  of  the  negative  ions  emitted  by  a  hot  carbon  filament 
was  determined  by  Sir  J.  J.  Thomson  in  1899. l  Two  parallel 
aluminium  plates  were  arranged  in  a  vessel  which  could  be  ex- 
hausted. A  small  incandescent  lamp  filament  was  fixed  between 
the  plates  and  close  to  one  of  them.  The  plate  near  the  filament 
was  negatively  charged,  and  the  current  carried  by  the  negative 
ions  from  the  filament  to  the  other  plate  was  measured.  When  a 
magnetic  field  was  produced  parallel  to  the  plates,  this  current 
was  diminished  if  the  field  was  greater  than  a  definite  value 
depending  on  the  potential  difference  and  distance  between  the 
plates.  From  the  values  of  these  quantities  the  ratio  e/m  was 
calculated,  and  found  to  be  about  9  X  106,  which  agrees  within 
the  errors  of  experiment  with  the  value  of  e/m  for  cathode  rays, 
or  negative  electrons.  For  the  negative  electricity  emitted  by  a 
glowing  Nernst  filament  Owen2  found  e/m  =  6  X  106,  and  for  that 

1  Phil.  Mag.  V.  48,  p.  547,  1899. 

2  Owen,  Phil  Mag.  VI.  8,  p.  230,  1904. 


6  ELECTRICAL  PROPERTIES   OF   FLAMES 

emitted  by  hot  lime  Wehnelt1  found  e/m  =  1*4  x  107.  O.  W. 
Richardson  2  has  recently  measured  e/m  for  the  negative  electricity 
emitted  by  hot  platinum  itself,  and  finds  it  equal  to  about  1*5  x 
<107.  Thus  it  is  clear  that  the  negative  electricity  is  emitted  as 
free  negative  electrons.  The  emission  of  these  electrons  by  many 
quite  different  substances  at  high  temperatures  affords  a 
convincing  proof  that  they  are  a  common  constituent  of  all  forms 
of  matter. 

In  discussing  the  discharge  of  electricity  from  hot  bodies,  it  is 
convenient  to  adopt  a  special  name  for  the  current  carried  by  the 
electrons  or  ions  emitted.  Following  Prof.  O.  W.  Richardson, 
I  shall  call  this  current  the  thermionic  current,  and  the  ions 
carrying  it  thermions. 

The  thermionic  current  obtained  in  a  good  vacuum  is  indepen- 
dent of  the  potential  difference,  provided  this  is  greater  than  a 
few  volts.  If  the  P.D.  is  very  small,  some  of  the  electrons 
which  escape  diffuse  back  to  the  wire,  so  that  the  current  is 
smaller. 

The  maximum  current  is  usually  called  the  saturation 
current. 

The  variation  of  the  thermionic  current  from  hot  platinum  in 
a  vacuum  with  the  temperature  of  the  platinum  was  first  investi- 
gated by  O.  W.  Richardson,3  who  at  the  same  time  put  for- 
ward an  elegant  theory  to  account  for  it,  which  is  now  firmly 
established. 

The  variation  of  the  thermionic  current  with  the  temperature 
is  shown  in  Fig.  2,  given  by  Richardson  (loc.  cit.). 

If  i  denotes  the  saturation  thermionic  current  per  sq.  cm.  of 
platinum  surface,  and  6  the  absolute  temperature,  then  Richardson 
found  i  =  A0*e-Q<2*,  where  A  and  Q  are  constants.  This  formula 
represents  the  curves  shown  in  Fig.  2  very  well. 

The  following  table,  taken  from  a  paper  by  the  writer,4  shows 
the  accuracy  with  which  Richardson's  formula  represents  the 

1  Wehneldt,  Ann.  d.  Phys.  vol.  xiv.  p.  425,  1904. 

2  Phil.  Mag.  (6)  vol.  xvi.  p.  740,  1908.     Ibid.  (6)  vol.  xx.  p.  545,  1910. 

3  Proc.    Camb.   Phil.  Soc.   vol.  xi.   p.  286,   1902.     Phil.  Trans,  vol.  201, 
p.  516,  1903. 

4  H.  A.  Wilson,  Phil  Trans,  vol.  202,  p.  243,  1903. 


DISCHARGE   OF  NEGATIVE   ELECTRICITY         7 

thermionic  current.     The  calculated  currents  are  those  given  by 
the  equation  i  =  6'9  X  1070*£-1310002'. 


Temperature. 


1375 

1408-5 

1442 

1476 

1510-5 

1545 

1580 


Current  per  sq.  cm.  found. 

Current  calculated. 

1-57  x  10-8 

1-49  x  10-8 

3-43 

" 

3-33 

7-46 

7'18 

15-2 

15-3 

32-3 

31-8 

63-8 

64-5 

128 

128-5 

According  to  Richardson's  theory  the  electrons  which  escape 
from  hot  bodies  are  those  which  are  contemplated  in  the  electron 


1200°       1250°        1300°      1350°        WOO0       W-5<j0  ,     I5OO°      1550° 
Temperature  Centigrade 

FIG.  2. 

theory  of  metallic  conductivity  and  heat  radiation.  A  metal  is 
supposed  to  contain  a  large  number  of  free  negative  electrons, 
which  move  about  inside  it,  colliding  with  the  metallic  atoms  just 


8  ELECTRICAL   PROPERTIES    OF    FLAMES 

as  the  molecules  of  a  gas  collide  with  each  other  on  the  kinetic 
theory  of  gases.  The  negative  charge  (Q)  carried  by  all  the  free 
electrons  in  one  c.c.  of  the  metal  is  equal  to  the  positive  charge  on 
the  atoms  in  one  c.c.  The  electrons  between  collisions  are 
supposed  to  move  freely,  and  their  mean  kinetic  energy  of  trans- 
lation is  taken  to  be  equal  to  that  of  a  gas  at  the  temperature  of 
the  metal.  The  distribution  of  velocities  among  the  electrons  is 
given  by  Maxwell's  well-known  law,  just  as  in  the  case  of  a  gas. 

At  the  surface  of  the  platinum  it  is  convenient  to  suppose  the 
existence  of  an  electrical  double  layer  in  accordance  with  the  usual 
theory  of  contact  potential  differences.  In  this  double  layer  the 
negative  charge  must  be  on  the  outside.  Let  the  fall  of  potential 
across  the  double  layer  be  99,  so  that  an  electron  in  escaping  from 
the  platinum  through  the  layer  must  do  work  (pe  ergs.  Conse- 
quently, if  the  velocity  of  an  electron  on  entering  the  layer  is  ^ 
perpendicular  to  the  layer,  and  v2  when  it  gets  out,  we  have 

i^Oi2  "  V)  =  <Pe 

In  going  through  the  layer  we  suppose  the  velocity  components 
parallel  to  the  layer  to  be  unchanged- 

Let  n  denote  the  number  of  free  electrons  per  c.c.  in  the  metal. 
Then,  according  to  Maxwell's  law,  the  number  dn  per  c.c.  which 
have  velocity  components  perpendicular  to  the  surface  of  the 
platinum  lying  between  v  and  v  +  dv  is  given  by 

dn  =  n 


where  q  =  3/2£2  and  v2  denotes  the  mean  value  of  the  square  of 
the  resultant  velocity  of  an  electron. 

Hence,  the  number  of  electrons  entering  unit  area  of  the 
double  layer  per  second  is 


nv(  -±]  e 

^7l< 


Of  these,  only  those  for  which  v  is  greater  than  ^/2tpe/m  will 
have  enough  energy  to  get  through  the  double  layer,  so  that  the 
number  escaping  per  second  is 


DISCHARGE   OF   NEGATIVE   ELECTRICITY        9 

where  i  denotes  the  thermionic  current  per  sq.  cm.,  and  e  the  charge 
carried  by  one  electron.  The  charge  e  is  4'9  X  10"10  E.S.  units, 
and  is  equal  to  the  charge  on  one  monovalent  ion  in  solutions. 

Let  N  denote  the  number  of  molecules  in  one  gram  molecular 
weight  of  any  gas,  and  let  Neq?  =  P,  so  that  P  is  the  work  required 
to  enable  N  electrons  to  escape.  Also,  let  the  mean  kinetic  energy 
of  an  electron  be  equal  to  a6,  where  a  is  a  constant  and  6  the 
absolute  temperature.  For  any  gas  R0  =  f  Na9,  where  R  denotes 

the  gas  constant  for  one  gram  molecule.     Also  q  =  ~' ,  : 

*«&*-* 

in         Ru 


I    R  6 
Hence —  i  =  nc  */  —  ^     e  - 

Now  R  for  one  gram  molecule  is  very  nearly  equal  to  two  small 

calories,  hence-       i  =  ne  ^J ^y     £-p2' (1) 

where  P  is  now  the  energy  in  small  calories  required  for  the 
escape  of  N  electrons. 

R 

~ — ^       this    equation     becomes 

i  =  D0^£  ~  p<2*,  which  is  of  the  same  form  as  the  equation  which 
we  have  seen  represents  the  observed  thermionic  currents.  How- 
ever, it  does  not  follow  that  D  =  A  and  P  =  Q,  as  might  be 
thought  at  first  sight ;  for  P  and  D  may  not  be  constants.  We 
have  D0*e-p-2'  =  A0*e  -  <*2«  or  P  =  Q  +  20%D/A,  so  that 
P  and  D  must  satisfy  this  equation.  P,  therefore,  must  be  equal 
to  Q  at  the  absolute  zero  of  temperature.  It  will  be  seen  in  the 
following  chapter  that  P  does  vary,  and  so  is  not  equal  to  Q  at 
high  temperatures.  D  also  is  not  equal  to  A. 

It  is  important  to  bear  in  mind  the  distinction  between  P  and 
Q  and  between  D  and  A. 

We  can  easily  show  that  the  distribution  of  velocities  among 
the  electrons  which  escape  is  the  same  as  among  those  which 
enter  the  double  layer.  The  number  entering  per  sq.  cm.  in  one 

V  =   GO 

second  is 

nv    (  — 


f    n 
*/,-o 


10         ELECTRICAL  PROPERTIES   OF  FLAMES 

so    that  the  fraction  2qve  ~qc~dv  have  normal  velocities  between 
v  and  v  +  dv.     The  velocity  of  these  after  passing  through  the 

layer  is      v*  --  "-\  so  that  the  number  escaping  with  velocities 


between  v  and  v  -f  dv  is 


If  we  divide  this  by  the  total  number  which  escape- 

n        ~2^ 


-  £ 


we  get  2^£  -9"2rft;,  the  same  as  for  those  which  enter  the  double 
layer. 

Consider  a  cone  of  small  solid  angle  dw  with  its  vertex  at  a 
small  element  of  area  ds  on  the  surface  of  the  hot  platinum.  Let 
the  angle  between  the  axis  of  the  cone  and  the  normal  to  ds  be  6. 
We  can  easily  show  that  the  number  of  electrons  emitted  by  ds 
which  move  off  inside  the  cone  is  proportional  to  cos  6.  Of  the 
electrons  emitted,  the  fraction  whose  three  velocity  components 
lie  between  u  and  u  -f  du,  v  and  v  +  dv,  and  w  and  w  +  dw 
respectively,  is  equal  to 

^-  £-*v2  du  civ  dw 
n 

where  V2  =  u2  -f  v2  -f-  iv2.     For  those  inside  the  cone  v  =  V  cos  d 
and  du  dv  dw  =  V2  dco  dV,  so  that  the  fraction  in  the  cone  is 

0 

da)  cos  6  ;-:  V  ' 


sddw  f 
n       J  ' 


o 

Suppose  we  have  a  plane  surface  of  hot  platinum,  and  parallel 
to  it  a  plane  conductor.  Let  the  conductor  be  charged  negatively, 
so  that  there  is  a  uniform  electric  field  between  the  platinum 
and  the  conductor.  If  the  difference  of  potential  between  the 
conductor  and  the  platinum  is  y,  then  only  those  electrons 
which  enter  the  double  layer  with  normal  velocity  greater  than 

*~^^  will  have  enough  energy  to  get  across  to  the  con- 
ductor.    The  current  to  the  conductor  will  therefore  be  given 

by 


DISCHARGE   OF  NEGATIVE   ELECTRICITY       11 


Hence- 


or 


ne 


(3) 


f-6 


-3  -4 

&truii 

FIG.  3. 

This  equation  has  been  tested  experimentally  by  Richardson 
and  Brown.1  Since  Ne  is  equal  to  the  charge  carried  by  one 
gram  molecule  of  monovalent  ions,  it  is  accurately  known.  The 
equation,  therefore,  was  used  by  Richardson  and  Brown  to  calcu- 

1  PM.  Mag.,  September  1908. 


12         ELECTRICAL  PROPERTIES   OF   FLAMES 

late  R  for  the  electrons.  The  values  they  obtained  were  ranged 
around  the  value  of  R  for  gases  at  the  temperature  6. 

The  agreement  of  the  formulae  (1)  and  (3)  with  the  experi- 
mental results  justifies  the  assumption  made  that  the  distribution 
of  velocities  among  the  electrons  is  that  given  by  Maxwell's  law. 

In  Richardson  and  Brown's  experiment  a  thin  flat  strip  of 
platinum  heated  by  a  current  was  placed  close  and  parallel  to  a 
plane  electrode,  and  the  thermionic  current  from  it  was  allowed 
to  slowly  charge  up  another  insulated  electrode  parallel  to  the 
first.  The  rise  of  the  potential  of  the  insulated  electrode  was 
measured  with  a  quadrant  electrometer. 

In  Fig.  3  the  curve  shows  the  relation  between  the  thermionic 
current  and  the  potential  difference,  while  the  straight  line  gives 
the  relation  between  the  logarithm  of  the  current  and  the  potential 
difference.  From  the  slope  of  the  straight  line  N0/R0  can  be 
immediately  obtained,  and  hence  R.  The  value  of  R  comes  out 
2 '2,  instead  of  the  theoretical  value  2. 

Richardson l  has  also  made  experiments  on  the  distribution  of 
the  velocity  components  parallel  to  the  surface  of  the  hot  platinum. 
In  these  experiments  a  narrow  strip  of  platinum  about  2  cms. 
long  was  mounted  in  a  slit  cut  in  a  plane  electrode,  so  that  the 
surface  of  the  strip  was  flush  with  that  of  the  electrode.  A 
second  plane  electrode  was  placed  parallel  to  the  first  and  about 
0*5  cm.  distant  from  it.  The  second  electrode  also  contained  a 
slit  parallel  to  the  platinum  strip,  and  the  current  carried  by  the 
electrons  emitted  by  the  platinum  which  entered  this  slit  was 
measured.  The  second  electrode  could  be  moved  parallel  to  the 
first  in  a  direction  perpendicular  to  the  slits.  The  whole  was 
contained  in  an  exhausted  vessel.  The  variation  of  the  charge 
entering  the  slit  in  the  second  electrode  as  this  was  moved  across 
in  front  of  the  hot  strip  was  determined. 

The  slit  in  the  movable  electrode  was  much  shorter  than  the 
hot  strip,  so  that  the  strip  could  be  regarded  as  of  infinite  length 
without  very  serious  error,  and  the  velocities  parallel  to  the  length 
of  the  strip  disregarded. 

It  will  suffice  to  consider  the  theoretical  distribution  in  two 

1  Phil.  Mag.,  December  1908. 


DISCHARGE    OF   NEGATIVE   ELECTRICITY       13 

cases,  first  when  the  potential  difference  between  the  electrodes  is 
large,  and  second  when  it  is  zero. 

In  the  first  case,  the  initial  velocity  of  the  electrons  perpen- 
dicular to  the  electrodes  can  be  neglected,  so  that  the  time  taken 
by  an  electron  to  go  across  to  the  movable  electrode  is  */2dm/Xe, 
where  d  is  the  distance  between  the  electrodes  and  X  the  electric 
field  strength.  For  Xe/m  is  the  acceleration  of  the  electrons. 

Let  u  denote  the  velocity  component  of  an  electron  in  a 
direction  perpendicular  to  the  length  of  the  strip  and  parallel  to 
the  electrodes.  Among  n  electrons  emitted,  the  number  for  which 
u  is  between  u  and  u  -j-  du  is  given  by 


Let  x  denote  the  displacement  of  the  movable  slit  from  the 
position  opposite  to  the  strip,  then  if  u\/2dm/X.e  =  x  the  electrons 
will  go  into  the  slit.  Hence  the  charge  entering  the  slit  will  be 
proportional  to  £-q€Xx2'2dm.  If,  then,  it  is  the  current  entering 
the  slit,  we  have 


where  i0  is  the  current  when  x  =  0.  Substituting  V/d  for  X  where 
V  is  the  P.D.  between  the  electrodes,  and  using  the  value  given 
above  for  q,  this  becomes 


The  following  table  is  taken  from  Richardson's  paper:  — 

±x(l  =  -0318cm.)  01234567 

+  ix  1-35  1-38  117   '75    '51    -34    19    '00 

-  ix  1-35  1-25  1-09    -85    -47    '30    '21    13 

ix  (calculated)  1-38  T31  110    '83    '56    '34    18    '09 

The  values  of  ix  (calculated)  are  those  given  by  the  equation 
ix  =  1-38  X  10  ~24*2.  Thus,  the  observations  agree  very  well  with 
the  theoretical  equation.  The  value  of  R  can  be  calculated  from 
the  results,  for  all  the  other  quantities  in  the  equation  are  known. 
In  the  above  experiment  V  =  10'6  x  108  E.M.  units,  Ne  =  9644 
E.M.  units,  0  =  1500  Abs.,  and  d  =  0'534  cm.  These  give  R  =  2'5 


14         ELECTRICAL  PROPERTIES   OF   FLAMES 

small    calories,   which   is   25    per   cent,    greater  than    the   true 
value. 

When  the  potential  difference  between  the  two  electrodes  is 
zero,  the  electrons  will  travel  in  straight  lines. 

Equation  (2)  shows  that  the  number  of  electrons  falling  on  an 
element  ds  of  the  slit  from  an  element  of  the  strip  is  proportional 
to  the  solid  angle  which  ds  subtends  at  the  element  of  the  strip, 
multiplied  by  cos  6.  If  we  take  the  strip  to  be  infinitely  long,  it 
follows  that  the  number  falling  on  the  slit  is  proportional  to  the 
angle  subtended  by  the  breadth  of  the  slit  at  the  strip  and  to 
cos  6.  Thus— 

^_       d 

--C(      = 


In  this  case,  also,  Richardson  1  found  the  observed  and  calculated 
currents  to  agree  as  well  as  could  be  expected. 

It  appears,  therefore,  that  the  theory  considered  leads  to  results 
which  agree  well  with  the  facts.  The  experiments  described  give 
a  striking  verification  of  Maxwell's  law  of  the  distribution  of 
velocities  among  the  electrons. 

The  formula  i  =  DO^e  ~  PI2e  can  be  obtained  thermodynamically 
if  we  assume  the  emission  of  the  negative  electrons  to  be  analogous 
to  the  evaporation  of  a  liquid.2 

If  p  is  the  vapour  pressure  of  a  liquid,  and  L  its  latent  heat  of 

evaporation  per  gram  molecular  weight,  then  L  =  (v.2  —  v^  6  -K* 
where  v2  =  volume  of  vapour  and  i>j  =  volume  of  liquid.  Neglect- 
ing vl  and  putting  v2  =  R0/p,  we  get  L  =  ^  •  Let  the  internal 
work  done  in  evaporating  the  liquid  be  P,  so  that  L  =  P  -f  T®  and 

p+at.-SfJ 

p    dO 
Hence  — 


Now  p  =  frtfiVN,  where  m  is  the  mass  of  a  molecule,  V  the 
square  root  of  the  mean  square  of  the  velocities  of  all  the  mole- 

1  Phil  Mag.,  November  1909. 

2  H.  A.  Wilson,  Phil  Trans.  A.  vol.  202.  pp.  243-275,  1903. 


DISCHARGE   OF   NEGATIVE   ELECTRICITY       15 

cules,  and  N  the  number  leaving  each  sq.  cm.  of  the  liquid 
surface  per  second,  and  I  a  constant.  But  V2  is  proportional  to  6, 
hence  we  may  write  p  =  b'N^O,  where  lf  is  a  constant.  Putting 
this  in  the  above  equation,  we  get — 

0i*N9  =  P/l 

But  i  =  Ne  and  R  =  2,  so  that 

OM9      P/l 


which  is  equivalent  to  *  =  D#*e  "  p  2e. 

For  pure  platinum  in  a  vacuum,  or  in  air  at  low  pressure, 
O.  W,  Richardson,  H.  A.  Wilson,  F.  Horton,  Deininger,1  and 
others  have  all  obtained  values  of  Q  differing  little  from  130,000. 
As  to  A,  however,  there  is  a  good  deal  of  doubt,  for  a  small  error 
in  the  currents  leads  to  a  large  error  in  A,  and  traces  of  hydrogen 
or  other  impurities  change  A  much  more  than  Q.  It  is  probable 
that  A  for  pure  platinum  is  not  much  less  than  108. 

1  Ann.  der  Phys.  IV.  vol.  xxv.  p.  304,  1908. 


CHAPTER  III 


THE  DISCHARGE  OF  NEGATIVE  ELECTRICITY  BY  HOT 
PLATINUM  IN  HYDROGEN  AND  OTHER  GASES. 

WHEN  platinum  is  heated  in  gases  such  as  oxygen,  nitrogen, 
or  helium,  which  have  little  or  no  action  on  it,  the  negative 
thermionic  current  is  not  directly  affected.1  The  potential 
difference  required  to  give  the  saturation  current  is  increased,  as 
we  should  expect.  If  the  electric  field  near  the  hot  wire  exceeds  a 
certain  value,  proportional  to  the  pressure  of  the  gas,  the  electrons 
acquire  sufficient  energy  to  ionize  the  molecules  with  which  they 
collide,2  so  that  then  the  current  is  increased  by  the  presence  of 
the  gas.  This  effect  led  some  experimenters  to  suppose  that  the 
gas  really  increases  the  number  of  electrons  emitted  by  the  wire, 
but  it  was  shown  by  the  writer  (loc.  cit.)  that  ionization  by 
collisions  is  sufficient  to  account  for  it. 

In  hydrogen,  however,  the  negative  thermionic  current  is 
greatly  increased,  even  when  the  hydrogen  is  only  present  in 
minute  quantities.3 

The  following  table  gives  the  currents  observed  when  success- 
ive small  quantities  of  pure  hydrogen  were  admitted  into  an 
apparatus  like  that  shown  in  Fig.  1.  The  temperature  of  the 
platinum  wire  loop  was  1350°  C. 


Pressure  of  Hydrogen  (p) 
mms.  of  Mercury. 

Thermionic  Current  (c) 
Scale  Divisions. 

(<1O»J5)--™ 

0-0006 

10 

2-65 

0-0015 

20 

2-70 

0-0033 

40 

3-01 

0-0053 

50 

2-65 

0-0080 

75 

2-92 

0-0140 

110 

2-85 

1  H.  A.  Wilson,  Phil  Trans.  A.  vol.  202,  p.  243,  1903  ;  F.  Horton,  Phil. 
Trans.  A.  vol.  207,  p.  149,  1908. 

2  J.  S.  Townsend,  The  Theory  of  Ionization  of  Gases  by  Collision. 

3  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  208,  p.  247,  1908. 

16 


DISCHARGE   OF   NEGATIVE   ELECTRICITY       17 

The  values  of  cp-'u  given  in  the  third  column  are  nearly 
constant,  showing  that  the  current  is  proportional  to  y74  at 
1350°  C.  The  current  from  a  clean  wire  at  1350°  C.  in  a  good 
vacuum,  when  all  traces  of  hydrogen  have  been  removed  by  letting 
in  air  and  pumping  it  out  several  times  with  the  wire  at  a  high 
temperature,  is  usually  not  more  than  1/250  in  the  units  used.  It 
appears,  therefore,  that  at  a  pressure  of  0'014  mms.  at  1350°  C. 
the  hydrogen  increases  the  thermionic  current  about  25000  times. 

It  is  very  difficult  to  get  rid  of  traces  of  hydrogen  in  highly 
exhausted  tubes,  so  that  it  often  happens  that  comparatively 
large  currents  are  obtained.  When  the  wire  is  heated,  hydrogen 
may  be  evolved  by  the  surrounding  electrode,  by  the  wire  itself, 
or  even  by  the  glass.  Since  oxygen  does  not  appear  to  affect  the 
negative  thermionic  current,  a  simple  way  of  getting  its  true 
value  in  the  absence  of  hydrogen  is  to  let  in  a  little  pure  oxygen 
or  air.  Any  hydrogen  present  is  then  burnt  up  at  the  hot  wire> 
and  the  water  vapour  formed  can  be  absorbed  by  phosphorus 
peutoxide.  The  potential  difference  used  must  riot  be  sufficient 
to  produce  ionization  of  the  oxygen  by  collisions. 

When  the  pressure  of  the  hydrogen  is  changed  the  resulting 
change  in  the  thermionic  current  does  not  all  occur  immediately, 
but  takes  time  to  become  established.  The  current  variation  lags 
behind  that  of  the  pressure.  The  same  thing  happens  when  the 
temperature  of  the  wire  is  altered  in  hydrogen  at  constant  pressure. 
This  clearly  indicates  that  the  increase  in  the  current  produced 
by  the  hydrogen  is  due  to  the  presence  of  hydrogen  in  the 
surface  of  the  platinum,  and  that  it  takes  time  for  the  equilibrium 
between  the  metal  and  the  gas  to  be  established  after  any  change 
in  the  conditions.  The  time  required  for  the  current  to  become 
constant  varies  considerably  with  the  temperature  and  pressure. 
Half  an  hour  is  usually  more  than  sufficient,  even  after  a  large 
change. 

At  constant  pressure  the  variation  of  the  equilibrium  current 
with  the  temperature  is  represented  approximately  by  the  for- 
mula i  =  A0*e  -Q/2d,  which  holds  good  in  a  vacuum.  The  following 
table  contains  values  of  A  and  Q  found  by  the  writer.1 

1  Phil.  Trans.  A.  vol.  208,  p.  249, 1908. 


18          ELECTRICAL  PROPERTIES   OF  FLAMES 


Gas. 

Pressure. 

Q. 

A. 

Aii- 

Small 

145,000 

1-14  x'10s 

Air 

Small 

131,000 

6-9     x  107 

H 

0-0013  mm. 

110,000 

10« 

H 

0-112  mm. 

90,000 

5  x  104 

H 

113-00 

56,000 

2  x  10- 

The  second  values  in  air  are  for  a  wire  which  had  been  boiled 
in  nitric  acid  for  one  hour,  and  the  first  for  one  boiled  in  nitric 
acid  for  twenty-four  hours.  In  both  cases  the  wire  was  heated 
strongly  while  air  was  let  in  and  pumped  out  several  times.  In 
the  second  case  it  seems  likely  that  a  minute  trace  of  hydrogen 
still  remained  in  the  wire. 

It  will  be  observed  that  the  hydrogen  diminishes  both  Q  and  A. 
At  constant  pressure  we  have  i  —  A0*e~Q2*,  where  A  and  Q  are 
functions  of  p,  and  at  constant  temperature  i  =  ~Bpn ,  where  B  and 
n  are  functions  of  6  only. 

Let  \  and  i2  be  the  currents  at  0X  and  02  when  the  pressure 
is  p.  Then — 


Now  let  if  and  i2  be  the  currents  at  61  and  02  when  the  pressure 
is  p'.     Then— 

a  rv'  /  1        1  \ 


where  Q'  is  the  value  of  Q  at  p'.     Also  let  it  =  Bx  pn\  if  =  B^/^, 
i.2  =  B2p«*t  and  i2  =  B2#/n*.     Hence — 


=  £ 


or 


!i.^_  =  (P 

",  -  nz  _  Q'  -  Q 


In  this  equation  the  right-hand  side  is  a  function  of  p  only, 
and  the  left  one  of  0  only.  Hence  both  sides  must  be  equal  to  a 
constant  a  say.  Consequently  n  =  a6~l  —  c  andQ  =  U  —  2alogp, 
where  c  and  U  are  constants.  If  these  values  are  put  in  the 


DISCHARGE   OF  NEGATIVE   ELECTRICITY        19 


equation  Bpn  =  A.6?s~Q'2e  we  easily  see  that  A  must   be  equal 
to  Kp  '  c,  where  K  is  a  constant. 

If  we  take  a  =  2400,  we  get  the  following  values  of  Q  +  2a 


P 
0-0013 

0-112 

133-0 


Q 
110,000 

90,000 
56,000 


u 

78,000 
79,500 
79,500 


If  we  take  C  =  0'73  we  get  the  following  values  of  A.pc  =  K. 

p  A  K 

0-0013  10°  7,800 

0-112  5  x  104  10,100 

133-0  2  x  102  3,600 

Thus,  while  p  is  increased  105  times,  U  remains  practically 
unchanged  and  K  only  varies  by  a  factor  of  3.  A  small  error  in 
the  observed  currents  produces  a  large  one  in  A,  so  that  this 
quantity  cannot  be  found  very  exactly.  It  seems,  therefore,  that 
the  values  found  for  A  and  Q  agree  well  with  the  assumption  that 
the  current  is  proportional  to  pn  at  constant  temperature. 

The    equations    A  =  Kp~c     and    Q  =  P  —  2a    log   p     give 

4(Q-p) 

A  =  Ke2a  .......     (1) 

Putting  U  =  79000,  a  =  2400,  K  =  9000,  and  c  =  073,  and 
calculating  Q  from  the  values  found  for  A,  the  following  results 
are  obtained  :  — 

Q  =  6580  log  A  +  19100. 


Gas. 

Pressure. 

A 

y 

(Calculated  ) 

Q 

(Found.) 

Air 
Air 
H2 

1 

Small 
Small 
0-0013 
0-112 
133-0 

1-14  x  10s 
7  x  107 
10° 
5  x  104 
2  x  10 

142,000 
138,000 
110,000 
90,300 
54,000 

145,000 
131,000 
110,000 
90,000 
56,000 

It  appears  that  this  relation  is  satisfied  by  the  values  of  A  and 
Q  for  a  wire  in  air,  as  well  as  by  those  for  the  wire  in  hydrogen. 

If  we  put  p  =  0  in  the  equations  Q  =  P  —  2a  log  p  and 
A  =  Kp~c  we  get  Q  =  oo ,  and  A  =  oo .  These  equations  there - 

C  2 


20          ELECTKICAL  PROPERTIES   OF  FLAMES 

fore  require  modifying  to  enable  them  to  represent  all  the  values 
of  A  and  Q.  If  we  suppose  A  =  A0/(l  -f  apc)  where  a  is  a 
constant,  then,  when  apc  is  large  compared  with  unity,  this 
formula  will  agree  with  A  =  Kp~c  and  when  p  =  0  it  gives 
A  =  A0.  We  have 

A0/          1-14  X  108 
/K=     9X10*      =  1'27) 

When  p  =  O'OOl,  apc  =  100,  so  that  even  at  this  pressure  the 
difference  between  the  two  formulae  is  only  one  per  cent. 

Equation  (1)  gives  A  =  A0fi2ifQ~Qo),  so  that 

Q  =  Q0  -  2CW-1  log  (1  +  ape). 

This  formula  gives  Q  =  Q0  when  p  ==  0,  and  for  all  measurable 
values  of  p  does  not  differ  appreciably  from 

Q  =  Qo  —  2a  l°g  P  —  %ac~l  log  a. 

When^>  =  1,  Q  =  U,  so  that  this  is  the  same  as  Q  =  U—  2a  log  p, 
which  has  been  shown  to  agree  with  the  values  found  for  Q  at 
different  pressures. 

If  we  substitute  the  values  found  for  A  and  Q  in  the  equation 
i  =  A0*£-Q/2«  we  get    . 


i  =  A0(l  +  apc)      "  *  Q 
If  p  =  0,  this  gives  iQ  =  A0<9*£  -  °-°/2<?, 

so  that  -A  =  (1  -f  apc)  (*  ~  ' 

?o 

which  gives  the  ratio  of  the  negative  thermionic  current  in  a 
vacuum  or  in  air  to  that  in  hydrogen  at  pressure  p.  Also  c  =  0'73, 
a  =  1-27  x  104,  and  a  =  2400. 

At  900°  C.,  in  hydrogen  at  26  mms.  pressure,  Richardson1 
found  i/i0  to  be  4  x  108.  The  above  equation  gives  2  x  109. 
Since  a  small  error  in  c  produces  a  large  error  in  i/i0  the 
agreement  in  this  case  is  as  good  as  could  be  expected.  Thus, 
if  we  take  c  =  0'78,  instead  of  0'73,  we  get  i/i0  =  3  x  10s. 

At  1570°  C.,in  hydrogen  at  760  mms.  pressure,  G.  H.  Martyn2 
found  i/i0  =4-4  X  104.  The  formula  gives  6'5  X  104.  At  1343°  C., 

1  Phil.  Trans.  A.  vol.  207,  p.  1,  1906.         2  Phil  Mac/.,  August  1907. 


DISCHARGE   OF  NEGATIVE   ELECTRICITY       21 

in  hydrogen  at  O'OOIS  mm.,  I  found  i/iQ  =  170.  The  formula 
gives  122. 

It  appears,  therefore,  that  the  equation — 

••     •-•  '..-.-•'      ^(i  +  opote-O    • 

represents  the  values  found  by  different  observers  as  well  as  could 
be  expected  for  pressures  from  zero  to  760  mms.,  and  for  tempera- 
tures from  900°  C.  to  1600°  C.  Within  these  limits  i/i0  varies  from 
unity  to  more  than  108.  It  seems  clear,  therefore,  that  the  equa- 
tions i  =  ~Bpn  and  i  =  A6?e  ~  Q/2fl  which  were  assumed  at  the  start 
are  very  approximately  true.  It  is  also  clear  that  the  thermionic 
current  has  a  definite  value  capable  of  being  reproduced  by 
different  observers. 

The  values  of  n  given  by  n  =  ad  - l  —  c  also  agree  within 
the  limits  of  error  with  those  calculated  directly  from  various 
observations.  It  is  important  to  observe  that  i/i0  diminishes 
rapidly  with  rising  temperature  :  thus  at  800°  C.  and  one  mm. 
pressure  i/i0  =  3'4  x  108,  while  at  1800°  C.  it  is  only  24  X  102. 

Since  the  thermionic  current  varies  continuously  with  the 
pressure  of  the  hydrogen,  it  follows  that  the  hydrogen  is  dis- 
solved in  the  platinum.  For  if  a  definite  compound  were  formed, 
then  if  the  pressure  were  above  its  dissociation  pressure,  com- 
bination would  be  complete,  and  the  state  of  the  platinum  would 
be  independent  of  the  pressure ;  while  if  the  pressure  were  less 
than  the  dissociation  pressure,  all  the  compound  would  decompose. 

According  to  the  theory  explained  in  the  first  chapter, 
the  constant  D  in  the  theoretical  formula  i  =  T>6^e~p/2e  is 
equal  to  ?^/v/R/2?rNm,  so  that  it  should  be  proportional  to  the 
number  (n)  of  free  electrons  per  c.c.  in  the  platinum.  We  have 
seen  that  A  in  the  experimental  formula  i  =  A0*e  ~ Q/2fl  may  be 
diminished  by  hydrogen,  from  108  to  102.  But  the  conductivity 
of  the  platinum  is  very  little  affected  by  the  hydrogen,  so  that  n 
must  really  be  practically  unchanged.  At  first  sight,  therefore, 
the  diminution  of  A  appears  to  be  incompatible  with  the  theory. 

Richardson l  pointed  out  that  if  Q  varies  with  the  tempera- 
ture, the  value  of  A  deduced  from  the  observed  currents  may 

1  Phil  Trans.  A.  vol.  201,  p.  497,  1903. 


22         ELECTEICAL  PROPERTIES   OF  FLAMES 


differ    greatly    from    the    theoretical    value    D  = 

Thus,  suppose   P  =  Q  +  aO.     Then   the   equation   i= 

becomes  i  =  Ds  -  °/2  0*e  -  Q/2', 

so  that  the  value  of  A  calculated  from  the  currents  is  De  -  a/2  and 

the  value  of  Q  calculated  is  not  equal  to  P. 

Equating  the  theoretical  and  experimental  expressions  for  the 
thermionic  current,  we  get 


or  P  =  Q  +  20  log  D/A   ......     (1) 

so  that  if  P  and  D  satisfy  this  equation,  then  the  observed 
currents  will  agree  with  the  formula  i  =  A0*e  "  Q/2d,  as  is  found  to 
be  the  case.  Consequently,  P  and  D  may  be  any  functions  of  0 
and  p  which  satisfy  (1),  and  yet  the  formula  i  =  A0*£~Q/20,  in  which 
A  and  Q  are  constants,  will  agree  with  the  observed  currents. 

According  to  the  electron  theory  of  metallic  conduction,  it  is 
probable  that  n  does  not  vary  very  much  with  the  temperature. 
The  conductivity  is  roughly  inversely  proportional  to  the  absolute 
temperature  for  most  metals.  According  to  the  electron  theory 
the  conductivity  is  proportional  to  ne2h/mV,  where  h  is  the  mean 
free  path  of  the  electrons.  Now  V  is  proportional  to  \f  6,  so 
that  if  1  is  independent  of  the  temperature,  this  requires  n  to  be 
inversely  proportional  to  >\/0  to  make  the  conductivity  inversely 
proportional  to  0.  In  the  measurements  of  the  thermionic  cur- 
rents the  range  of  temperature  is  not  very  large  usually,  so  that 
the  variation  of  \/0  is  comparatively  small.  Consequently,  we 
may  suppose  n  to  be  independent  of  0  without  serious  error. 

If  we   suppose  that  n  and   so   D   are   independent   of   the 
temperature,  then,  according  to  the  theory, 
P  =  Q  +  20  log  D/A 

must  increase  uniformly  with  0.  According  to  this  view,  the 
changes  in  A  with  the  pressure  of  the  hydrogen  are  to  be 
ascribed  to  the  variation  of  P  with  the  temperature,  and  not  to 
any  change  in  D.  Also  it  follows  that  the  number  of  electrons 
per  c.c.  cannot  be  even  roughly  calculated  from  the  value  found 
for  A.  In  order  to  get  D  and  P  it  is  necessary  to  make  some 
hypothesis  to  explain  the  variation  of  P  with  the  temperature.1 
i  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  208,  p.  247,  1908. 


DISCHARGE   OF  NEGATIVE   ELECTRICITY       23 

To  explain  the  energy  necessary  to  enable  an  electron  to 
escape  from  the  platinum  we  supposed  that  an  electrical  double 
layer  exists  at  the  surface.  Let  this  consist  of  an  infinitely  thin 
layer  of  electricity  at  a  distance  t  from  the  platinum,  having  a 
charge  o  per  sq.  cm.  If  no  electrons  were  present  the  difference 
of  potential  between  the  layer  and  the  platinum  would  be  4>7iot  ; 
but  actually  electrons  will  be  present  in  between  the  layer  and 
the  platinum,  and  will  increase  the  electric  force.  This  effect  will 
increase  as  the  temperature  rises,  so  that  if  P  is  due  to  such  a 
layer,  it  will  vary  with  the  temperature. 

Let  n  denote  the  number  of  electrons  per  c.c.  at  a  point  at 
a  distance  x.  from  the  platinum.  Let  p  denote  the  gas  pressure 
due  to  the  electrons,  and  p  denote  the  electric  volume  density 
so  that  p  =  ne.  Then  when  there  is  equilibrium  we  have 
—  dpjdx  -f-  Fp  =  0,  where  F  denotes  the  electric  force  inside  the 
double  layer.  Now,  at  the  layer  of  electricity  p  is  very  small, 
since  only  a  minute  fraction  of  the  electrons  escape,  consequently 
at  x  =  t  F  =  —  4jra  and  dF/dx  =  0. 

Let  p  =  —  /3p,  where  /?  is  a  constant  at  constant  temperature, 
so  that 


ft 
dx  ~    dx  ~  4>n  dxz' 

Hence-  £*  +  Ff  =  0, 

r  dx2          dx 

yri 

which  gives  f}—  —  j-  JF2  =  c. 

When  x  =  t  this  becomes     c  =  8^2o2, 

so  that  tifS-  -f  F2  =  16jiV. 

^  dx 

Integrating,  this  gives 

F  =  (F0_+ 

a       (F0.+ 
where  a  =  4jra. 

At  x  =  0  p  =  Po,  so  that  8jrft>0  +  F02  =  a2.     Now  F0  will  be 
nearly  equal  to  —  a,  so  that  this  gives  approximately 


24         ELECTRICAL  PROPERTIES    OF   FLAMES 

Hence-  J_-  =  87ro*  * 

This  gives  V  =  --  f¥dx  = 

-  ft  log  (l  +  ~  e  -  **«»  +  -$* ,  fi*« 

V  Pn/5  167T02 


In  this  equation  the  terms — 
«  R 

frat/fii  =  10-14)f 


are  quite  negligible  compared  with  --  f-4^/^  =  1014),  so  that 

PoP 
we  get 


which  gives,  putting  ft  =  ft06, 

V  =  knot  +  2ft00  log  ^: 


P,  the  work  in  calories  required  for  N  electrons  to  escape, 
is  equal  to  NeV/J,  where  J  is  the  mechanical  equivalent  of  heat  ; 
also,  since  P  =  Q  when  6  =  0,  we  can  put  Q  =  knotNejJ  and  so 
obtain 

2 
=  Q- 


/        2/8tf^rfVN«\ 

~Q^ 


CompariDg  this  with  P  =  Q  +  20  log  D/A  we  get 

.      D  N. 


Since  j9  =  —  pftQ6  =  —  ^^00  wre  see  that  —  /?0eN  is  equal  to 
the  gas  constant,  hence  ftQe~N/J  =  —  2  calories.     Hence  — 


If  we  take  two  values  of  Q,  C^  and  Q2,  and  the  corresponding 
values  Al  and  A2,  we  get 
_ 


DISCHARGE   OF   NEGATIVE   ELECTRICITY       25 

This  equation,  with  the  values  found  for  A  and  Q,  gives 
D  =  3-7  x  108. 

Having  found  D  we  can  use  it  to  calculate  the  value  of  ne.    We 

have  D  =  ne^     ^    .    Here  R  =  8'4  x  107  ergs,  N«  =  9644  E.M. 

units,  and  e/m  =  1*7  X  107  in  E.M.  units  as  for  cathode  rays. 
Putting  in  these  values  and  D  =  3*7  x  108,  we  get  ne  =  2'4  x  103 
coulombs,  or  7'2  X  1012  E.S.  units.  Since  e  is  equal  to  4*9  x  10 -10 
E.S.  units,  this  gives  n  =  1*5  x  1022  free  electrons  in  one  c.c.  of 
platinum. 

The  number  of  atoms  of  platinum  in  one  c.c.  is  6  x  1022,  so 
that  there  is  one  free  electron  for  every  four  atoms. 

The  expression  for  t  then  gives  the  following  values : — 


Q                                     A 

t 

145,000 
131,000 
110,000 
90,000 
56,000 

1-14  x  108 
6-9     x  107 
106 
5  x  104 

2  x  102 

9-6  x  10-8  cm. 
9-9 
107 
9-0 
5-6 

The  five  values  of  t  agree  as  well  as  could  be  expected. 

It  is  interesting  to  apply  the  formula  for  t  to  platinum 
polarised  with  hydrogen  in  dilute  sulphuric  acid.  The  potential 
fall  in  this  case  is  about  0'9  volt,  which  corresponds  to  a  value 
of  Q  about  2-1  x  104.  If,  then,  we  suppose  A/D  to  be  small, 

Q2g 

which  is  the  case  in  hydrogen  at  high  pressures,  we  get  f2  =  ^    ™ 

which  gives  at  6  =300,  t  =  4r8  X  10  ~8.  The  thickness  of  the 
double  layer  in  this  case  has  been  estimated  by  several  observers 
from  the  polarisation  capacity,  and  found  to  be  about  2  x  10  ~8  cm. 

Thus  the  theory  proposed  leads  to  probable  values  of  the 
thickness  of  the  double  layer  and  of  the  number  of  free  electrons 
per  c.c.  in  the  platinum,  so  that  it  seems  adequate  to  explain  the 
facts. 

Substituting  the  values  found  for  A,  Q  and  D  in  the  formula 
P  =  Q  "4-  20  log  D/A,  we  get  the  following  values  of  P : — 


26         ELECTRICAL  PROPERTIES   OF  FLAMES 


Gas. 

Pressure, 

P. 

Air 



145,000+    2-350 

H2                                    0-0013 

110,000  +  11-830 

H2                                    0-112 

90,000  +  17-820 

H2                                133-0 

56,000  +  28-860 

Thus,  in  air  P  only  varies  very  slowly  with  the  temperature. 

It  appears,  therefore,  that  the  thickness  t  of  the  double  layer 
on  the  platinum  is  unchanged  by  the  hydrogen,  which,  however, 
diminishes  the  fall  of  potential  across  it.  This  effect  may  be  due 
to  positively  charged  hydrogen  atoms  in  the  double  layer,  but  the 
precise  way  in  which  the  hydrogen  acts  is  unknown. 

In  some  experiments  Richardson l  found  that  the  leak  from  a 
hot  platinum  wire  in  hydrogen  was  independent  of  the  pressure, 
even  when  this  was  reduced  to  a  very  small  value.  The  writer2 
found  that  this  is  always  the  case  after  a  wire  has  been  heated  in 
hydrogen  at  a  comparatively  high  pressure  for  some  time.  After 
this  treatment  the  properties  of  the  wire  are  completely 
changed. 

The  wire,  then,  gives  a  large  thermionic  current  practically 
independent  of  the  pressure  of  the  hydrogen,  from  760  mms.  down 
to  less  than  O'OOl  mm. 

The  following  table  gives  the  currents  observed  from  a  wire 
treated  in  this  way,  at  a  pressure  of  O'OOS  mm.  : — 


Temperature. 


1578°  C. 
1613°  C. 
1648°  C. 
1683°  C. 


Amperes  per  sq.  cm. 


9-51  x  10-5 
19-26       „ 
38-7 
723 


These  numbers  give  A  =  1*67  x  1010,  and  Q  =  135300.  The 
value  of  Q  is  thus  nearly  the  same  as  for  a  wire  in  air,  but  A  is 
100  times  larger. 

If  the  wire  is  heated  in  air  or  oxygen  the  large  thermionic 
current  immediately  disappears.  It  can  also  be  made  to  disappear 


1  Phil.  Trans.  A.  vol.  207,  p.  1,  1906. 

2  Phil  Trans.  A.  vol.  208,  p.  247,  1908. 


DISCHARGE   OF  NEGATIVE   ELECTRICITY       27 

by  heating  above  1700°  C.  in  a  very  high  vacuum.  These  facts 
make  it  very  probable  that  the  hydrogen  combines  with  the  wire, 
forming  a  very  stable  compound.  This  compound  must  have  a 
very  small  dissociation  pressure.  It  must  also  be  formed  very 
slowly,  unless  the  pressure  of  the  hydrogen  is  high. 

After  the  wire  has  been  heated  in  oxygen  it  gives  the  same 
thermionic  currents  as  an  ordinary  wire  in  which  the  compound 
has  never  been  formed.  However,  a  permanent  effect  seems  to 
remain,  for  the  time  lag  of  the  current  after  changes  of  pressure 
seems  much  greater  than  before. 

Richardson  found  that  increasing  the  potential  difference  from 
19  volts  to  286  volts  caused  the  negative  leak  in  hydrogen  at 
1-77  mms.,  at  1084°  C.  to  diminish  gradually  from  147  x  10~8  to 
26  x  10  ~8  ampere.  This  effect,  he  suggested,  may  be  due  to  the 
bombardment  of  the  wire  by  the  positive  ions  produced  by  ionisa- 
tion  by  collisions  due  to  the  high  potential.  This  bombardment 
may  remove  the  hydrogen  atoms  in  the  double  layer,  and  so  make 
the  negative  current  correspond  with  that  due  to  hydrogen  at  a 
lower  pressure. 

The  writer  found  that  a  wire  in  hydrogen  giving  a  negative 
current  which  was  slowly  increasing  with  the  time,  gave  less 
current  at  high  temperatures  than  at  low.  The  current  was 
saturated  and  rose  when  the  temperature  was  diminished. 

These  peculiar  effects  seem  to  take  place  only  when  the  wire  is 
not  in  equilibrium  with  the  hydrogen.  Further  investigation  is 
required  to  find  out  their  cause. 

Other  substances  besides  hydrogen  have  been  found  to  increase 
the  negative  thermionic  current.  Thus  the  writer  noticed  a  great 
increase  due  to  phosphorus  pentoxide.1  A  systematic  examination 
of  the  effects  of  a  large  number  of  different  substances  might  lead 
to  interesting  results. 

1  Phil.  Trans,  vol.  202,  p.  243. 


CHAPTER   IV 


THE  DISCHARGE  OF  NEGATIVE   ELECTRICITY  BY 
VARIOUS  SUBSTANCES 

O.  W.  RICHARDSON1  investigated  the  negative  thermionic 
current  from  carbon  and  sodium,  as  well  as  from  platinum.  Both 
these  substances  gave  very  large  currents.  Sir  J.  J.  Thomson  2 
found  the  current  from  sodium  to  be  greatly  increased  by  the 
presence  of  hydrogen,  so  that  it  could  be  observed  even  at  ordinary 
temperatures. 

Wehnelt3  discovered  that  the  oxides  of  the  alkaline  earths 
emit  a  copious  supply  of  negative  electrons  when  heated  in  a 
vacuum.  Owen4  measured  the  negative  thermionic  current 
from  a  Nernst  lamp  filament.  In  all  these  cases  the  formula 
i  =  A0*£~Q/2*  was  found  to  represent  the  variation  of  the  current 
with  the  temperature. 

The  following  table  gives  the  values  found  for  Q  and  A.  Q  is 
expressed  in  calories  per  gram  molecule  of  electrons,  and  A  so  as 
to  give  the  current  in  amperes  per  sq.  cm. 


Substance. 

Q 

A 

Carbon 

19-6  x  10* 

1015 

Sodium 

6-3     „ 

102 

Baryta 

9        „ 

7  x  107 

Lime 

8-6     „ 

5  x  107 

Nernst  filament 

9-2     „ 

7  x  104 

Owen  (loc.  cit.)  examined  the  effect  of  a  transverse  magnetic 
field  on  the  negative  thermionic  current,  and  found  that  a  part  of 
it  was  carried  by  heavy  ions  not  easily  deflected  by  the  field. 
With  platinum  at  1300°  C.,  95  per  cent,  of  the  current  could  be 
deflected  by  a  small  field,  and  therefore  was  carried  by  electrons. 

1  Phil  Trans.  A.  vol.  201,  p.  516,  1903.     In  these  early  experiments  traces 
of  hydrogen  or  other  impurities  were  probably  present  and  caused  a  very  great 
increase  in  the  thermionic  currents.  See  Pring  and  Parker,  Phil. Mag.,  Jan.  1912. 

2  Conduction  of  Electricity  through  Gases,  p.  203. 

3  Ann.  d.  Phys.  (4)  vol.  xiv.  p.  425,  1904. 

4  Proc.  Camb.  Phil  Soc.  vol.  xii.  p.  493,  1904.     Phil.  Mag.  (6)  8,  230,  1904. 

28 


DISCHARGE    OF   NEGATIVE   ELECTRICITY       29 


With  new  wires  the  percentage  of  heavy  ions  was  greater  than 
with  wires  which  had  been  heated  for  some  time. 

Felix  Jentzsch l  measured  the  negative  thermionic  current 
from  a  number  of  metallic  oxides  in  a  vacuum.  He  found  the 
following  values  of  Q  and  A.  The  constant  A  gives  the  current 
per  sq.  cm.  in  electrostatic  units. 


Substances. 

Q 

A 

BaO 

83-2  x 

10-'5 

141.x  1 

Q15 

SrO 

89-8      , 

152       , 

) 

CaO 

80-6      , 

129       , 

I 

MgO 

79-0      , 

1  x  1 

Oio 

BeO 

47-8      , 

0-31 

Y903 

72-6      , 

' 

5590 

_  —  :  — 

La263 

75-8      , 

» 

207 

A19O3 

74-6      , 

j 

2 

ZrO9 

73-2 

1970 

ThO9 

71-2 

10-5 

CeOo 

74-2 

586 

ZnO 

70-2 

0-092 

Fe20o 

93-8 

1076 

Nil)' 

102-4 

8370       , 

i 

CoO 

99-4 

1595       , 

CdO 

60-4 

0-11     , 

) 

CuO 

45-0      , 

> 

O'OOl 

) 

It  will  be  observed  that  Q  does  not  vary  very  much,  whereas 
A  varies  very  greatly. 

Jentzsch  pointed  out  that  the  possible  error  in  Q  was  two  or 
three  per  cent.,  while  that  in  A  was  as  much  as  500  per  cent. 
Consequently,  it  is  very  difficult  to  get  more  than  the  order  of 
magnitude  of  A. 

For  lanthanum  oxide  he  gives  the  following  table :— 


Absolute  Temperature. 

Current  (Calculated). 

Current  (Found). 

Percentage  difference. 

1355 

133 

12-2 

8 

1405 

367 

35-5 

3 

1450 

86-2 

82-4 

4 

1470 

124 

132 

6 

1510 

249 

256 

3 

1570 

662 

692 

4 

1625 

1525 

1515 

1 

1680 

3325 

3065 

8 

1720 

5700 

7160 

26 

Inaugural  Dissertation,  Berlin,  1908 


30         ELECTRICAL   PROPERTIES   OF   FLAMES 

The  calculated  currents  are  those  given  by  the  equation— 

i  =  516  x  lO^e-75800-'2' 

Jentzsch  found  the  currents  in  all  cases  to  obey  the  same 
law. 

The  copious  emission  of  negative  electrons  by  lime  can  be 
shown  very  clearly  by  means  of  a  vacuum  tube  fitted  with  a 
•"  Wehnelt  cathode."  This  consists  of  a  strip  of  platinum  foil 
which  can  be  heated  to  incandescence  by  passing  a  current 
through  it.  On  the  foil  is  a  small  patch  of  lime,  obtained  by 
putting  a  drop  of  dilute  calcium  nitrate  solution  on  it  and  then 
heating.  The  tube  is  provided  with  another  electrode  to  serve  as 
anode.  If  a  moderate  P.D. — say  200  volts — is  maintained  between 
the  anode  and  cathode,  then  on  heating  the  cathode,  a  narrow 
stream  of  cathode  rays  is  emitted  by  the  patch  of  lime.  If  the 
pressure  is  not  too  low,  the  path  of  this  stream  through  the  tube 
is  visible  as  it  emits  a  faint  blue  light.  The  deflection  of  the 
stream  by  magnetic  and  electric  fields  can  be  easily  demonstrated 
owing  to  the  low  P.D.,  so  that  such  a  tube  is  very  useful  for 
showing  the  properties  of  cathode  rays. 

Sir  J.  J.  Thomson  found  that  a  good  way  of  making  the  patch 
of  lime  is  to  put  a  very  small  bit  of  sealing-wax  on  the  foil  and 
then  heat  it.  The  wax  contains  lime,  or  baryta,  and  gives  a  firmly 
adherent  patch. 

Hydrogen  increases  the  current  from  lime  in  the  same  way  as 
from  platinum.  Thus,  G.  H.  Martyn  *  calculated  the  following 
negative  thermionic  currents  at  1600°  C.  from  observations  at 
different  temperatures : — 

Platinum  in  air   .         .         .         .     5  x  10  ~7  ampere 
Lime  in  air.         .         .         .         .     5  x  10 ~2       „ 
Platinum  in  hydrogen .         .         .  10 -1 

Lime  in  hydrogen        .         .         .  103         „ 

F.  Horton  2  gives  the  following  values  of  the  constants  Q  and 
A  found  in  helium  at  a  few  mms.  pressure  : — 

Platinum         .         .         .     T22  x  105  T6  X  106 

Calcium  ....     7'29  x  104  17  X  104 

Lime       .         .         .         .     9'58  x  104  6'4  x  1011 

-  *  Phil.  Mag.,  August  1907.          2  Phil.  Trans.  A.  vol.  207,  p.  149,  1908. 


DISCHARGE   OF   NEGATIVE   ELECTRICITY       31 

He  observed  that  the  current  from  lime  is  greatly  increased 
by  hydrogen. 

The  conductivity  of  metallic  oxides,  like  lime,  is  small  at  low 
temperatures,  but  increases  rapidly  with  the  temperature. 

The  variation  of  the  conductivity  (a)  with  the  temperature l  is 
given  at  any  rate  roughly  by  the  formula  o  —  Ke~S2d,  where  K 
and  S  are  constants.  Hence,  we  have  approximately  D  =  Be~s/2fl; 
so  that  i  =  B0*e-<p  +  s>;2«. 

It  follows  from  this  that  the  value  of  Q  calculated  from  the 
currents  observed  at  different  temperatures  with  metallic  oxides 
is  not  P  but  P  -f-  S.  Also,  the  value  found  for  A  is  equal  to 
B  =  De~s-'M.  Thus,  if  n  for  metallic  oxides  is  calculated  from  the 
values  found  for  A,  as  was  done  by  several  observers,  it  must  be 
wrong  by  the  factor  s'~S2e,  which  usually  amounts  to  many 
thousands.2 

O.  W.  Richardson  3  pointed  out  that  the  escape  of  negative 
electrons  from  hot  bodies  should  be  accompanied  by  an  absorption 
of  heat,  just  as  in  the  analogous  case  of  the  evaporation  of  a 
liquid. 

;  -  The  calculation  given  at  the  end  of  Chap.  I  shows  that  the 
latent  heat  of  emission  of  one  gram  molecule  of  electrons  is 
P  -f-  R0,  so  that  the  determination  of  this  latent  heat  affords  a 
method  of  finding  P  not  Q.  Wehnelt  and  Jentzsch  4  found  that 
the  current  required  to  keep  a  platinum  wire  coated  with  lime 
hot  was  greater  when  it  was  charged  negatively  and  emitting 
electrons  than  when  it  was  charged  positively  so  that  the  electrons 
were  prevented  from  escaping.  From  the  difference  between  the 
two  currents  the  heat  rendered  latent  was  calculated,  and  was 
compared  with  the  theoretical  amount  calculated  from  the  thermi- 
onic current  and  the  known  value  of  Q  for  lime.  The  observed 
values,  however,  came  out  several  times  larger  than  those  calcu- 
lated. This  is  especially  remarkable,  because  the  value  of  P  must 
be  considerably  smaller  than  the  value  of  Q  calculated  from  the 
thermionic  currents,  which,  as  we  have  seen,  is  equal  to  P  -f-  S. 

1  F.  Horton,  Phil  Mag.,  April  1906. 

2  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  208,  p.  247,  1908. 

3  Phil.  Trans.  A.  vol.  201,  p.  497,  1903. 

4  Ann.  d.  P/iys.  vol.  28,  p.  537,  1909. 


32         ELECTRICAL  PROPERTIES   OF  FLAMES 

The  reason  for  the  discrepancy  is  not  known.  Possibly  it  is  merely 
due  to  unavoidable  errors  in  measuring  such  small  quantities. 
Further  experiments  are  desirable  to  clear  up  this  question. 

When  the  electrons  emitted  by  a  hot  body  are  absorbed  by  a 
cold  electrode  we  should  expect  an  evolution  of  heat.  This  effect 
was  observed  by  Richardson  and  Cooke.1  The  cold  electrode  used 
by  them  was  a  strip  of  platinum,  and  the  heat  developed  was 
estimated  from  its  change  of  resistance  due  to  the  rise  in  tempera- 
ture. They  measured  the  heat  developed  in  the  platinum  strip 
when  it  had  been  treated  with  nitric  acid  to  remove  hydrogen,  and 
also  when  it  had  been  saturated  with  hydrogen.  In  the  first  case 
the  mean  value  of  P  deduced  from  the  observed  heating  effects 
was  128,000,  and  in  the  second  case  105,000.  The  temperature  of 
the  cold  electrode  was  probably  not  more  than  500°  Absolute, 
so  that  to  compare  the  values  found  for  P  with  those  calculated 
from  the  thermionic  currents  we  require  the  values  at  about 
500°  Abs. 

The  value  of  P  for  pure  platinum  given  by  the  expression 
P  =  145000  +  2-35(9  at  500°  Abs.  is  146,000,  which  does  not  differ 
much  from  128,000.  Also,  145,000  is  rather  higher  than  the  value 
of  Q  found  by  most  observers,  which  is  about  130,000,  which  would 
make  P  at  500°  Abs.  131,000.  For  platinum  in  hydrogen  at  133 
mms.  P  =  56000  +  28'860.  This  makes  P  at  500°  Abs.  equal  to 
70,000,  which  is  rather  less  than  Richardson  and  Cooke's  value 
105,000.  For  hydrogen  at  0112  mm.  P  at  500°  Abs.  comes  out 
99,000  and  so  agrees  very  well  with  105,000.  It  seems  likely  that 
though  the  platinum  strip  was  saturated  with  hydrogen,  before 
putting  it  in  the  apparatus  most  of  the  hydrogen  must  have 
escaped  when  the  pressure  was  reduced  to  a  small  value.  Con- 
sequently, the  amount  remaining  in  the  platinum  may  very  likely 
have  been  about  that  corresponding  to  a  pressure  of  0*112  mm. 

It  will  be  observed  that  since  Q  is  only  equal  to  P  at  0°  Abs., 
it  is  not  correct  to  compare  the  value  of  P  deduced  from  the  heating 
effect  directly  with  Q. 

It  is  clear  that  Richardson  and  Cooke's  experiments  are  in 
excellent  agreement  with  the  theory,  which  thus  receives  an 
interesting  confirmation. 

1  Phil  Mag.,  July  1910. 


CHAPTER   V 

THE  DISCHARGE  OF   POSITIVE  ELECTRICITY 
BY  HOT   BODIES. 

A  POSITIVE  charge  escapes  from  hot  bodies  in  air  at  a  rate 
which  increases  rapidly  as  the  temperature  rises. 

The  negative  thermionic  current  is  very  little  affected  by  the 
presence  of  air,  and  is  much  smaller  than  the  positive  current 
unless  the  pressure  is  very  low  or  the  temperature  very  high. 
The  variation  of  the  positive  thermionic  current  from  hot  platinum 
in  air  at  atmospheric  pressure,  with  the  temperature,  was  investi- 
gated by  the  writer  in  19011. 

The  apparatus  used  consisted  of  a  platinum  tube  0'75  cm.  in 
diameter,  which  was  heated  in  a  gas  furnace.  Along  the  axis  of 
this  tube  a  platinum  electrode  12  cms.  long  and  0*3  cm.  in 
diameter  was  supported,  and  the  current  between  the  electrode 
and  tube  through  the  air  was  measured.  A  constant  current  of 
air  could  be  passed  through  the  tube  during  the  measurements. 
The  temperatures  of  the  tube  and  electrode  were  measured  by 
means  of  thermo-couples.  Fig.  4  shows  the  relation  between  the 
current  and  potential  difference  observed  with  this  apparatus  at 
1080°  C.  without  any  current  of  air  through  the  tube. 

When  the  inside  electrode  was  positively  charged  the  current 
was  nearly  saturated  with  200  volts,  but  when  the  tube  was 
positive  it  continued  to  increase  up  to  800  volts.  When  the 
inside  electrode  is  positive,  the  ions  start  from  it  and  move  across 
to  the  tube,  so  that  they  start  in  the  strong  electric  field  close  to 
the  electrode,  whereas  when  the  current  is  reversed  they  start  in 
the  weaker  field  at  the  tube.  Also,  owing  to  the  greater  area  of 
the  surface  of  the  tube,  the  current  from  it  is  larger  and  so  more 
difficult  to  saturate.  In  this  experiment  with  no  air  current  the 
electrode  was  colder  than  the  tube,  which  also  helps  to  explain  the 
larger  current  from  the  tube. 

The  potential  difference,  about  1000°  C.,  could  not  be  raised 
much  above  800  volts  without  an  arc  forming  between  the  elec- 

1   Phil.  Trans.  A.  vol.  197,  pp.  415-441,  1901. 
D  33 


34         ELECTRICAL  PROPERTIES   OF  FLAMES 


trodes.  Thus  the  P.D.  required  to  produce  saturation  is  not  very 
much  less  than  that  required  to  spark  through  the  gas.  It  was 
found  that  on  heating  the  tube  and  putting  on  the  P.D.  a  large 
current  was  obtained  at  first,  which  rapidly  fell  off  and  settled 
down  to  a  nearly  constant  value  in  one  or  two  minutes.  After 


40O   CeLLs. 
800   Votts.) 


FIG.  4. 


standing  cold  for  some  hours  this  initial  large  current  could 
always  be  obtained.  The  initial  current  was  often  ten  times  the 
steady  current. 

The  steady  current  was  found  to  diminish  gradually  from  day 
to  day.     The  following  numbers  illustrate  this  effect : — 


Date. 

Temperature  900°  C. 

Temperature  1100°  C. 

July    6 
„     10 

„     30 

40  x  10  -  6  ampere 

11     „ 
0-7     „ 

400  x  10  -  6  ampere 

140     „ 

»     » 

DISCHARGE   OF   POSITIVE   ELECTRICITY        35 

Fig.  5  shows  the  variation  of  the  current  with  the  temperature, 
using  240  volts  with  the  inside  electrode  positive,  so  that  the 
current  was  saturated.  Fig.  6  shows  the  same  thing  with  40  volts, 
for  which  the  current  was  nearly  proportional  to  the  voltage.  In 
these  experiments  a  rapid  current  of  air  was  passed  through  the 
tube.  This  kept  the  inside  tube  hot,  and  also  served  to  blow  out 


700 


7,000°          /,/00°     .    7,200°       7,300  C. 

Temperature* 


FIG.  5. 


the  platinum  dust  which  is  emitted  at  high  temperatures.  If  this 
dust  is  allowed  to  accumulate  in  the  air  near  the  platinum,  the 
ions  get  stuck  to  it,  which  makes  it  more  difficult  to  saturate  the 
current.  In  a  good  vacuum  there  is  practically  no  permanent 
positive  thermionic  current  from  hot  platinum,  so  that  we  may 
D  2 


36 


ELECTRICAL   PROPERTIES   OF   FLAMES 


conclude  that  the  steady  current  obtained  Is  due  to  the  presence 
of  the'  air.  The  fact  that  the  positive  current  is  very  large 
compared  with  the  negative  current,  unless  the  temperature  is 
very  high,  shows  that  the  ions  are  formed  at  the  surface  of  the 
platinum. 


Ampe 


Temper&ture. 


FIG. 


The  precise  way  in  which  the  positive  ions  are  formed  is 
unknown,  but  if  we  regard  the  emission  of  positive  ions  as 
analogous  to  evaporation,  then  the  calculation  given  at  the  end  of 
Chap.  I  can  be  applied,  so  that  we  should  expect  the  saturation 
current  carried  by  the  positive  ions  to  be  given  by  the  equation 
i  =*  A.&E  ~ Q  ?6,  where  A  is  a  constant  and  Q  the  apparent  energy 


DISCHARGE   OF   POSITIVE    ELECTRICITY        37 

rendered  latent  by  the  production  of  one  gram  molecule  of  ions. 
This  equation  represents  the  variation  of  the  current  due  to  240 
volts  with  the  temperature  shown  in  Fig.  5  fairly  well  if  Q  is 
taken  equal  to  50,000.  The  variation  of  the;  jeurrent  due  to 
40  volts  with  the  temperature  shown  in  Fig.  6  gives  values  of 
Q  which  diminish  as  the  temperature  rises  from  36,000  at  $75°  C- 
to  25,000  at  1300°  C. 

The  heat  rendered  latent  by  the  production  of  ions  at  the 
surface  of  hot  platinum  was  first  calculated  from  the  variation  of 
the  thermionic  current  in  air  with  the  temperature  by  the  writer 
in  1901  (loc.  cit.).  It  was  then  supposed  that  the  air  molecules 
dissociated  into  positive  and  negative  ions  at  the  surface  of  the 
platinum,  and  that  there  was  an  equilibrium  between  the  ions 
and  undissociated  molecules.  On  this  supposition  the  formula 
i  =  A0*e~Q-'4*,  where  i  is  the  current  due  to  a  small  P.D.,  was 
deduced  by  the  application  of  the  thermodynamical  theory  of 
chemical  equilibrium.  The  current  due  to  a  small  P.D.  was 
taken  to  be  proportional  to  the  concentration  of  the  ions  at  the 
surface  of  the  platinum.  With  this  formula  the  currents  in  Fig.  6 
give  values  of  Q  ranging  from  71,000  at  975°  C.  to  49,000  at 
1,300°  C.  It  is  clear  now  that  the  theory  just  mentioned  is. 
inadequate,  because  according  to  it  we  should  expect  the  air. 
to  produce  a  negative  thermionic  current  equal  to  the  positive  < 
one,  which  is  not  found  to  be  the  case.  The  analogy  with 
evaporation  enables  the  formula  i  —  DO^s  ~ p  20  to  be  deduced 
without  making  any  supposition  as  to  the  precise  way  in  which 
the  ions  are  produced,  but  this  formula  is  only  applicable  to  the 
saturation  currents. 

Various  suppositions  can  be  made  to  explain  the  formation  of 
the  positive  ions.  We  may  suppose  that  the  air  molecules  lose  a 
negative  electron  to  the  hot  platinum  when  they  collide  with  it 
with  a  normal  velocity  greater  than  a  definite  value.  In  this 
way  the  formula  i  =  D0*e  -  p/2e  can  easily  be  obtained  as  for  the 
negative  electrons  escaping  from  the  platinum. 

Just  as  in  the  case  of  the  negative  electrons,  the  values  of 
A  and  Q  calculated  from  the  observed  currents  are  not  necessarily 
equal  to  the  values  of  D  and  P.  According  to  the  supposition  just 
mentioned,  D  ought  to  be  equal  to  ne^/R/ZnmN,  where  n  is  now 


38          ELECTRICAL  PROPERTIES   OF   FLAMES 

the  number  of  molecules  in  one  c.c.  of  the  air,  and  m  the  mass  of 
an  air  molecule. 

Another  view  which  may  be  taken  is  that  there  is  a  layer  of 
positively  charged  atoms,  or  molecules,  of  the  gas  on  the  surface 
of  the  platinum,  held  in  position  by  the  attraction  due  to  their 
charges.  These  atoms,  of  course,  tend  to  acquire  the  amount  of 
kinetic  energy  corresponding  to  the  temperature,  and  when  one 
gets  more  than  a  certain  amount  we  may  suppose  it  escapes. 
According  to  this  view  we  should  expect  the  negative  thermionic 
current  to  be  increased  by  the  presence  of  the  gas,  which  is  not 
the  case,  except  with  hydrogen. 

Another  view,  proposed  by  O.  W.  Richardson,  is  that  the  gas 
molecules  dissociate  to  some  extent  into  atoms  which  combine 
with  the  platinum.  The  compound  formed  dissociates  into 
platinum  and  positively  charged  atoms  of  the  gas.  The  pressure 
of  the  atoms,  on  this  view,  is  proportional  to  the  square  root  of  the 
pressure  of  the  undissociated  gas.  On  this  view,  at  low  pressures 
the  current  should  be  nearly  proportional  to  the  square  root  of 
the  pressure,  and,  at  high  pressures,  nearly  independent  of  the 
pressure,  because  then  the  combination  between  the  platinum  and 
oxygen  is  complete.  If  the  dissociation  into  atoms  were  complete 
the  current  would  be  proportional  to  the  pressure  at  low  pressures. 

It  will  be  convenient  now  to  consider  the  relation  between  the 
current  and  the  potential  difference  between  the  electrodes. 

In  the  case  of  two  concentric  cylinders,  the  electric  force  F  is 
given  by  the  equation  — 

4-  (Fr)  =  4>nor 
dr 

where  Q  is  the  density  of  the  electrification  in  the  gas.  The 
current  c  is  equal  to  ZnrYqk,  where  k  is  the  velocity  of  the  ions 
due  to  unit  field.  Hence  — 

d     ,,  4er 


so  that  (Fsrs)«  -  (F.r^  =       (r*  -  r,«) 

where  F2  is  the  field  at  radius  r2  and  Fl  that  at  rr 

This   equation   shows    that    the   electric   field   will    not    be 


DISCHARGE   OF  POSITIVE   ELECTRICITY        39 

2c 
appreciably  changed  by  the  ions  so  long  as  ^-  (V22  —  r^)  is  small 

compared  with  Fr. 

If  the  field  is  only  slightly  altered  by  the  ions  we  may  write — 

Yr  =  F^  +  <5(Fr) 
where  d(Fr)  is  a  small  quantity.     Hence — 

<5(Fr)  -  27r£1(r2  -  ri2)  =  ^F 
where  pl  is  the  density  of  electrification  at  rr 

If  dV  denotes  the  change  in  the  P.D.  due  to  the  ions,  we 
have,  when  the  inside  electrode  is  positive, 

dV  =f"2dVdr  =  Wr/  -  r*  -  2r*  logjj) 
J  n  ?i7 

taking  r.,  to  be  the  radius  of  the  outer  tube  and  i\  that  of  the 
inner.     Hence — 


In  the  same  way,  when  the  outside  tube  is  positive, 

Tn 


Putting  in  rz  =  O375  and  i\  =  0'15  cm.,  this  becomes 

A7       0146c 

V  =  --  ,  —  h  0'436^2. 

^2/t 

The  curve  with  the  outside  tube  positive,  shown  in  Fig.  4, 
can  be  represented  very  well  from  200  to  800  volts  by  an  equation 
of  the  form  V  =  Ac  +  B,  where  A  and  B  are  constants.     From 
this  curve  we  get  B  =  0'436^2  =  0'5  E.S.  units,  so  that 
gz  =  1-15  E.S.  units. 


Also,  since         =  A  =  and         =  10  ~5  in  the  straight 

dc  JcQ2  dc 

part  of  the  curve,  we  get 

k  =  1-3  X  104  in  E.S.  units 
or  k  =  43  cms.  per  sec.  per  volt  per  cm. 

The  curve  with  the  inside  electrode  positive  can  also  be  repre- 
sented by  V  =  Ac  +  B  between  20  and  100  volts,  but  B  is  too 
small  to  be  estimated  accurately. 

The  current  at  the  inside  electrode  when  it  is  positive  is  equal 
to  2nrlQlk¥r  The  relation  between  F  and  the  current  density  i 


40          ELECTRICAL  PROPERTIES   OF  FLAMES 

was  given  by  Sir  J.  J.  Thomson. l  If  there  are  n  ions  per  c.c. 
close  to  the  electrode,  the  number  striking  it  per  sec.  per  sq.  cm.  is 
nV/^/6n,  where  V  is  the  velocity  of  agitation  of  the  ions,  accord- 
ing to  the  kinetic  theory  of  gases.  If  we  suppose  that  when  an 
ion  strikes  the  platinum  it  gives  up  its  charge,  then  we  have 

neV 

I /==  * 

x/w& 

where  I  denotes  the  saturation  current  per  sq.  cm.     Also,  i  — 
and  k  =  l'4eA/mV,  so  that 

IF 


"\72 

—  ;:  —  is  independent  of  the  temperature,   and   A  for  a  molecule 

of  nitrogen   at  0°  C.   and  760   mms.  is  9'5  X  10  ~6  cm.      Also 

rnriV2     3p      ,  .    ,,  .  .  . 

-  =  -£-,  where  p  is  the  pressure  of  a  gas  containing  n  molecules 

per   c.c.     For    a    gas    at   atmospheric   pressure,  p  =  1*01  X  10°, 

•m  V2 
and  ne  =  2'6  x  1010,  so  that   -        —=-  =  2    E.S.  units.     Hence 


IF  I  —  i 

i  =  =p-^_-g»  and  since  i  =  Q-JeF^  we  get  Q  =  -—  -.      If  s  denotes 

the  saturation  current  per  cm.,  then  s  =  2jrr1I,  also  c  =  Zytr^  and 
k  =  1*3  x  104.  Substituting  these  values  in  the  expression 
found  for  V  and  the  values  of  i\  and  r9  we  obtain  — 


which  gives  V  in  E.S.  units.  The  saturation-current  per  cm.  for 
the  curve  in  Fig.  4  is  5'6  X  104  E.S.  units.  So  that  for  this 
curve — 

V  =  0-275^-  +  (l  -  --)  x  0-056. 

s  —  c      \         s  / 

The   following    table   gives   values   of    V    calculated    by   this 
equation,  and  also  the  observed  values  of  c/s  taken  off  the  curve  : — 

1  Conduction  of  Electricity  through  Gases,  p.  208,  1906. 


DISCHARGE   OF   POSITIVE   ELECTRICITY        41 


c's 

V  in  volts  (Calculated). 

c  s  (Found). 

o-i 

24-3 

0-12 

0-2 

34-2 

0-22 

0-3 

47-1 

0-30 

0-4 

65-1 

0-40 

0-5 

91 

0-63 

0-6 

131 

0-68 

0-7 

197 

0-82 

0-8 

333 

0-86 

0-9 

744 

0-9 

Owing  to  the  small  scale  of  Fig.  4,  the  values  of  cl*  could 
not  be  read  off  very  exactly,  so  that  the  agreement  between 
column  one  and  column  three  is  as  good  as  could  be  expected,  and 
provides  an  interesting  confirmation  of  Sir  J.  J.  Thomson's  theory 
of  the  relation  between  the  current  and  the  electric  force.  It  is 
plain  that  the  value  of  k  deduced  from  the  currents  with  the 
outer  electrode  positive  is  consistent  with  the  currents  with  the 
inside  electrode  positive. 


Since     = 


value  of  F  required  to  make  i  90  per 


cent,  of  I  is  18  E.S.  units,  or  5400  volts  per  cm.  The  value 
of  F  required  to  spark  through  air  at  1000°  C.  is  probably 
about  6500  volts.  It  was  found  that  the  potential  difference 
could  not  be  increased  much  above  800  volts  without  an  arc 
forming,  which  agrees  with  this  estimate.  Thus,  to  completely 
saturate  the  current  was  impossible,  although  the  electrodes 
were  only  two  or  three  mms.  apart,  because  the  necessary  field  is 
greater  than  that  required  to  spark  through  the  gas.  Neverthe- 
less, the  current  was  75  per  cent,  of  the  saturation  current  with 
only  200  volts,  which  is  only  one-quarter  of  the  P.D.  required  to 
spark. 

IF 

According  to  the  equation  'i  =  „  ----  =^7:  - 

F  +  mV2/l  ' 

of  i/I  is  independent  of  the  temperature,  so  that  we  should 
expect  the  variation  of  the  current  due  to  a  small  electric 
force  with  the  temperature  to  be  the  same  as  for  the  saturation 
currents.  Provided  that  the  electric  field  is  not  appreciably 


the  value 


42         ELECTRICAL  PROPERTIES   OF   FLAMES 

disturbed  by  the  ions,  we  should,  therefore,  expect  the  current 
due  to  a  small  P.D.  to  be  proportional  to  the  saturation  current. 
The  current  due  to  40  volts  increased  less  rapidly  with  the 
temperature  than  the  current  due  to  240  volts,  especially  at  the 
higher  temperatures.  This  is  probably  due  to  the  disturbance  of 
the  electric  field  by  the  ions,  which,  although  small  at  1000°  C.y 
increases  rapidly  with  the  temperature. 

l'4e/l 
The  formula  k  =  —  ^-  gives  k  =  65  cms.  per  sec.  for  one  volt 

per  cm.  for  a  nitrogen  molecule  in  air  at  atmospheric  pressure 
at  1000°  C.  This  agrees  as  well  as  could  be  expected  with 
the  value  of  k  found  above.  That  slow  ions  were  not  formed  by 
the  ions  sticking  to  platinum  dust  from  the  electrodes,  was  due 
to  the  dust  being  blown  out  by  the  air  current,  and  to  the  tube 
having  been  heated  for  long  periods  before  the  measurements 
described  were  made. 

Rutherford  1  measured  the  thermionic  current  from  a  sheet  of 
platinum,  heated  by  passing  a  current  through  it,  to  a  parallel 
electrode  in  air  at  atmospheric  pressure.  He  found  the  positive 
current  diminished  at  high  temperatures,  and  showed  that  this 
was  due  to  the  presence  of  slowly  moving  ions  which  were  formed 
•  in  increasing  numbers  as  the  temperature  rose.  He  determined 
the  velocity  of  the  ions,  and  found  it  fell  off  with  the  distance 
from  the  hot  plate.  At  several  cms.  distance  it  was  about  1*9 
cms.  per  sec.  for  one  volt  per  cm.  This  is  not  far  from  the 
velocity  of  the  ions  produced  in  air  by  Rontgen  rays,  which  are 
probably  single  molecules  of  oxygen  or  nitrogen.  The  very  slow 
ions  which  were  present  at  the  higher  temperatures  are,  no  doubt, 
formed  by  gas  ions  sticking  to  platinum  dust.  Near  the  hot  plate 
the  ions  had  much  larger  velocities  than  1'9. 

If  X  denotes  the   electric  force  in  the  air  between  the  hot 

TAT 

platinum  sheet  and  the  parallel  electrodes,  then  ^—  =  4>nQ,  where 

x  is  the  distance  from  the  sheet  and  Q  the  density  of  electrification 
in  the  air.  The  current  per  sq.  cm.  (i)  is  equal  to  7^X,  so  that 


Physical  Review,  vol.  xiii,  p.  321,  1901. 


DISCHARGE   OF   POSITIVE   ELECTRICITY        42 

If  we  assume  that  k  is  independent  of  x  and  the  same  for  all 
the  ions,  we  get — 


If  I  is  the  distance  between  the  plate  and  electrode,  and  V  the 
potential  difference,  then 

fti        &  I78*^  ,   \*'*     3/2l 

V=y^=sldAT-+V      -C    \ 

When  x  =  0,  we  have  X0  =  \/c.  When  the  current  is  small 
compared  with  the  saturation  current  we  may  take  it  to  be 
proportional  to  X0,  so  that  i  =  £X0,  where  £  is  a  constant.  Hence 

k   [78m/. 
"  12mlA  k        . 
When  i  is  so  small  that  i2/fP  and  is/f}B  can  be  neglected,  this 
gives  approximately 

3/2 


so  that  the  current  is  proportional  to  V2  and  inversely  proportional 
to/3. 

Rutherford  found  that  this  equation  represented  his  experi- 
mental results  fairly  well  when  /  was  not  less  than  two  or  three 
cms.,  so  that  his  currents  were  extremely  small  compared  with 
the  saturation  currents. 

When  I  is  small,  and  i  not  too  small,  the  equation  (1)  reduces 
to 

I  . 


which  is  of  the  same  form  as  we  found  for  cylindrical  electrodes 
when  the  electric  field  was  not  much  affected  by  the  ions.  This 
equation  obviously  affords  a  simple  method  of  finding  7c. 

TT 
According  to  the  equation  -y  =  ^  —  ~,  which  we   have   seen 

represents  the  variation  of  the  current  with  the  electric  force 
at  the  surface  of  the  platinum,  F  must  be  equal  to  6  E.S.  units 
for  i  to  be  75  per  cent,  of  I. 

To  calculate  the  P.D.  required  to  give  about  75  per  cent,  of 
the  saturation  current,  therefore,  we  may  piit  X0=>v/c  =  6;  so 
that 


44         ELECTRICAL  PROPERTIES   OF   FLAMES 


If  i  =  10  -6  ampere,  or  3000  E.S.  units,  I  =  5  cms.,  k  =  3  x  10s. 
This  gives 

V  =  14700  volts. 
If  I  =  042  cm.,  we  get 

V  =  336  volts. 

OO/' 

In  this  case   the  average  electric  force  Qy^  -  ^TO  =  6*1  E.S. 

' 


O 

X  0'2 

units,  is  nearly  equal  to  X0>  so  that  the  electric  field  is  practically 
unaffected  by  the  presence  of  the  ions. 

It  is  only  when  i  is  a  small  fraction  of  the  saturation  current 
that  the  electric  field  is  appreciably  disturbed  by  the  charge  in 
the  gas. 

It  has  been  suggested  that  in  my  experiments  the  current 
was  always  very  far  from  saturation,  so  that  the  variation  of  the 
current  with  the  temperature  was  due  to  the  variation  of  the 
velocity  of  the  ions,  and  not  to  the  variation  of  the  ionization. 
That  this  was  not  the  case  is  obvious  from  the  fact  that  the 
current  was  nearly  saturated  with  200  volts,  and  was  proportional 
to  the  P.D.  up  to  about  100  volts.  Also  the  value  of  Q  calculated 
from  the  saturation  currents  agrees  with  the  result  obtained  by 
O.  W.  Richardson  with  entirely  different  apparatus. 

In  Rutherford's  experiments  the  variation  of  the  current 
with  temperature  was  largely  due  to  the  variation  of  the  velocity 
of  the  ions,  and  was  entirely  different  from  the  variation  with 
temperature  in  my  experiments.- 

The  initial  large  positive  thermionic  current  mentioned  above 
was  found  by  O.  W.  Richardson  l  to  occur  with  a  new  platinum 
wire  in  a  vacuum,  and  to  be  proportional  to  s~af,  where  t  denotes 
the  time,  and  a  is  a  constant.  .  The  value  of  a  depends  on  the 
temperature  and  other  conditions.  This  suggests  that  this  initial 
current  is  due  to  the  presence  of  some  substance  which  disappears 
at  a  rate  proportional  to  the  amount  of  it  present.  It  disappears 
almost  completely  after  heating  a  new  platinum  wire  for  a  short 
time  in  a  vacuum,  but  it  can  be  made  to  reappear  by  allowing  the 

1  Phil.  Mag.,  July  1903. 


DISCHARGE   OF  POSITIVE   ELECTRICITY        45 

platinum  to  be  exposed  to  the  air  in  a  room.  Richardson  1  found 
it  reappeared  if  the  wire  was  exposed  to  a  luminous  discharge  or 
heated  in  any  of  the  commoner  gases. 

W.  Wilson  2  found  that  heating  the  platinum  in  the  presence 
of  water,  or  dipping  it  in  water,  caused  it  to  afterwards  give  a 
large  positive  current  when  heated  in  air  at  atmospheric  pressure. 
He  also  found  that  the  decay  of  the  initial  positive  current  only 
goes  on  while  the  current'  is  flowing  and  not  while  the  hot 
platinum  is  surrounded  by  an  insulated  electrode. 

Sir  J.  J.  Thomson  3  measured  elm  for  the  positive  ions  from 
hot  platinum  in  air  at  a  low  pressure. 

A  strip  of  platinum  foil  was  arranged  parallel  to  an  insulated 
electrode,  and  3  mms.  from  it.  The  strip  could  be  heated  by  an 
alternating  current  and  raised  to  any  desired  potential.  The 
electrode  and  strip  were  contained  in  an  exhausted  tube  contain- 
ing air  at  a  low  pressure.  A  magnetic  field  could  be  applied 
parallel  to  the  surfaces  of  the  strip  and  electrode  and  the  current 
carried  by  the  positive  ions  from  the  strip  to  the  electrode  was 
measured.  It  was  found  that  a  magnetic  field  of  strength  19,000 
completely  stopped  the  current  with  a  potential  difference  of  3  or 
4  volts,  but  only  diminished  it  by  75  per  cent,  with  10  volts. 
The  effect  of  the  magnetic  field  was  not  appreciable  with  a 
potential  difference  above  120  volts. 

If  x  is  the  distance  of  an  ion  from  the  hot  strip,  X  the  electric 
force  parallel  to  x,  and  H  the  magnetic  force  parallel  to  the  axis  of 
z,  then 

d?x      v        TT  dy  ,1N 

md?  =  x-e+HeTt-  •;•-•  •;•  •  (1) 

d2y  dx  x 


dy 

or  m-r-  =  —  ricx 

at 

since  -j-  —  0  when  x  =  0  ;  hence,  from  (1)  — 
ctt 

<Fx  ,  HV 

M  -TT^  ~\  --  %   =   A.6 

dt2-         m 

1  Phil  Mag.,  September  1904.  2  Ibid.,  April  1911. 

3  Conduction  of  Electricity  through  Gases,  p.  220,  1906. 


46         ELECTRICAL   PROPERTIES    OF   FLAMES 

dx 

<n 


Integrating   from   x  =  0   to   x  =  d,  and    putting         =  0   at 


x  =  0  and  at  x  =  d,  we  get 
1  HW2 


in 


=  V 


where  d  is  the  distance  from  the  strip  to  the  electrode,  and  V  the 
difference  of  potential  between  them.     Hence  — 

e_        2V 

m 


{M  'IT 

The  assumption  that  —  =  0   at  x  =  d  means  that  the  ion 

considered  just  reaches  the  electrode.  Hence,  if  V  is  diminished, 
or  H  increased,  then  the  ions  do  not  get  across  to  the  electrode. 
Sir  J.  J.  Thomson  found  25  per  cent,  got  across  with  V  =  10, 
H  =  19000,  d  =  0*3  cm.  Hence,  for  the  75  per  cent,  stopped— 

-<  60 
m  = 

The  magnetic  field  had  some  effect  with  V  =  120,  so  that 
some  ions  were  present,  for  which 

-=720 
m 

For  hydrogen  ions  in  solutions  c/m  =  9644,  so  that  if  we 
assume  the  positive  ions  from  the  strip  carry  the  same  charge,  we 
get  for  the  atomic  weights  of  these  ions  about  170  and  13*4. 
These  results  indicate  that  most  of  the  ions  consisted  of  atoms  of 
platinum  and  some  of  oxygen,  or  nitrogen,  atoms.  Sometimes 
Sir  J.  J.  Thomson  found  the  current  practically  unaffected  by  the 
magnetic  field,  even  when  V  was  only  one  volt  or  less,  which 
indicated  that  the  ions  were  very  heavy  particles,  probably 
platinum  dust.  It  is  clear,  therefore,  that  at  high  temperatures 
some  of  the  positive  thermionic  current  may  be  carried  by  atoms 
of  the  hot  metal,  and  some  of  it  by  the  gas  present.  Rutherford 
(vide  supra)  also  found  heavy  ions  at  high  temperatures,  besides 
others  due  to  the  air.  At  high  pressures  the  current  due  to  the 
gas  is  very  large  compared  with  that  due  to  the  metal. 

Sir  J.  J.  Thomson  1  also  measured  e/m  for  the  positive  ions 

1  Conduction  of  Electricity  through  Gases,  p.  148,  1906. 


DISCHARGE   OF  POSITIVE   ELECTRICITY        47 

from  an  iron  wire  at  a  very  low  pressure,  and  found  it  equal 
to  400,  which  makes  the  atomic  weight  24  on  the  assumption  that 
the  charge  is  equal  to  that  on  an  hydrogen  atom  in  solutions. 

O.  W.  Richardson1  measured  e/m  for  the  positive  ions  emitted 
by  platinum  in  a  vacuum,  and  found  e/m  =  384.  With  carbon 
he  got  e/m  =  353. 

In  Richardson's  experiments  the  ions  from  a  hot  strip  placed 
in  a  uniform  electric  field  perpendicular  to  its  surface  were 
deflected  by  a  magnetic  field  which  was  parallel  to  the  length  of 
the  strip.  The  ions  from  the  strip  were  received  on  a  plane 
electrode  perpendicular  to  the  electric  field.  This  electrode  con- 
tained a  slit  parallel  to  the  hot  strip,  and  the  number  of  ions 
which  entered  this  slit  was  measured,  as  well  as  the  total  number. 
The  electrode  and  slit  could  be  moved  in  a  direction  perpendicular 
to  the  electric  and  magnetic  fields.  With  no  magnetic  field 
the  slit  received  a  maximum  fraction  of  the  ions  when  it  was 
opposite  the  strip,  and  with  a  magnetic  field  the  position  of 
this  maximum  was  deflected  through  a  distance  which  was 
determined. 

Let  the  distance  from  the  strip  to  the  electrode  be  d  and  the 
electric  field  Z.  Then  the  time  t  taken  by  the  ions  to  go  a 

V^ifflZ 
-y-  •     As  they 

move  across  they  are  acted  on  by  a  sideways  force  Rev  due  to 
the  magnetic  field  H.  Here  v  denotes  their  velocity  parallel  to 

Zet 

the  electric  field,  so  that  v  =  —  .     If  x  denotes  the  deflection  due 

tn 

to  the  magnetic  field— 

dzx 


m 

.J 

— 


TT  rr   0/3  .J 

which  gives         2    =  x  for  —  =  0  and  x  =  0  when  t  =  0.   Putting 


in  t  =  'y  -Tgr  and  Z  =  -£,  this  gives  x  =  "g^V"~^»  where  V  is  the 


P.D.  between  the  strip  and  electrode. 

In  the  above  calculation  we  have  neglected  the  force  on  the 

1  Phil.  Mag.,  November  1908. 


48         ELECTRICAL   PROPERTIES   OF  FLAMES 

ion  due  to  its  motion  in  the  magnetic  field  in  the  direction  of  x, 
but  in  Richardson's  experiments  the  deflection  x  was  small  conl- 
pared  with  d,  so  that  this  is  allowable.  In  his  experiments  d  was 
about  0'6  cm.  and  x  about  O'l  cm.  V  varied  from  55  to  341  volts, 
and  H  from  1200  to  4670. 

Richardson  also  measured  e/m  for  the  negative  electrons  from 
hot  platinum  in  this  way,  and  got  it  equal  to  1*45  x  107.  Thus 
it  appears  that  e/m  for  the  positive  ions  emitted  by  iron,  platinum 
and  carbon  in  a  vacuum  was  about  350  to  400  in  these  experi- 
ments. This  gives  about  26  for  the  atomic  weight  of  these  ions 
if  we  assume  that  they  carry  the  same  charge  as  a  monovalent 
ion  in  solutions.  It  is  evident,  therefore,  that  they  are  not  atoms 
of  the  hot  substance.  It  seems  likely  that  they  may  be  sodium 
atoms,  or  molecules  of  carbon  monoxide,  which  are  nearly  always 
present  in  vacuum  tubes  at  low  pressures,  especially  in  the 
presence  of  large  pieces  of  metal. 

In  a  later  paper  Richardson  and  Hulbirt l  give  the  results  of 
measurements  of  c/m  for  positive  ions  from  Pt,  Au,  Ag,  Cu,  Fe, 
Os,  Ta,  W,  brass,  nichrome  and  steel.  For  all  these  substances 
e/m  came  out  nearly  equal  to  400. 

Richardson  and  Brown  2  have  made  several  sets  of  measure- 
ments on  the  kinetic  energy  and  velocity  distribution  of  the 
positive  thermions  similar  to  their  measurements  on  the  negative 
electrons,  described  in  Chap.  I.  The  results  obtained  in  general 
agree  with  the  kinetic  theory,  as  in  the  case  of  the  negative 
electrons. 

The  following  table  gives  the  values  of  the  gas  constant  for 
one  c.c.  of  any  gas  calculated  from  their  observations  on  the 
variation  of  the  positive  thermionic  current  from  a  hot  plate  to  a 
parallel  electrode  with  the  P.D.,  by  means  of  the  theoretical 
formula — 

w»£_N* 


1  Phil.  Mag.,  October  1910. 

2  Ibid.,  December  1908,  March  1909,  October  1909. 


DISCHARGE   OF   POSITIVE   ELECTRICITY        49 


Substance. 

.  

Temperature. 

Gas  Constant/103. 

Platinum 

1193 

4-0 

5  7 

1067 

3'5 

?5 

1293 

3-5 

Gold  (1) 

(1030-973) 

4-2 

.,    (2) 

(1190-1163) 

3*9 

Silver  (1) 

1020 

3-0 

»     (2) 

1150 

2-9 

Palladium 

1170 

3-4 

Al  Phosphate  (1) 

1230 

3-9 

„      (2)    ! 

1170 

3-4 

Nickel 

1120 

3-6 

Iron  (1) 

1100 

4-6 

„     (2) 

1100 

5-2 

»     (3) 

1240 

4.4 

The  theoretical  value  of  the  gas  constant  for  one  c.c.  under 
standard  conditions  is  3'7  x  103.  The  values  found  in  a  few  cases 
differ  a  good  deal  from  the  theoretical  value,  but,  taken  together, 
the  results  show  that  the  average  energy  of  the  positive  ions  is 
nearly  equal  to  that  of  a  gas  molecule  at  the  temperature  of  the 
hot  body,  and  also  that  the  velocity  distribution  among  the  ions 
is  that  given  by  Maxwell's  law. 

When  the  initial  current  has  disappeared  there  is  little  or  no 
positive  current  in  a  good  vacuum.  In  gases,  however,  a  perma- 
nent positive  thermionic  current  remains,  which  depends  on  the 
pressure  and  nature  of  the  gas. 

The  writer l  found  the  following  positive  thermionic  currents 
from  a  platinum  wire  at  1300°  C.  in  hydrogen  : — 


Pressure. 


Current. 


766  mms. 

40  x 

10~9  amperes 

156     „                                    24 

55                     55 

9     „ 

4 

55                     5» 

These  numbers  indicate  that  at  high  pressures  the  current 
only  increases  slowly  with  the  pressure. 

In  comparing  the  positive  thermionic  currents  due  to  different 
gases,  it  is  important  to  remember  that  the  relative  values  may 
change  rapidly  with  the  temperature.  If  Q  in  one  gas  is  greater 
1  Phil.  Trans.  A.  vol.  202,  p.  243,  1903. 


50         ELECTRICAL  PROPERTIES   OF   FLAMES 

than  in  another,  then  the  current  due  to  the  first  gas  may  be 
negligible  compared  with  that  due  to  the  second  at  low  tem- 
peratures, but  enormously  greater  at  high  temperatures.  For 
example,  Richardson  found  the  current  in  hydrogen  less  than 
that  in  oxygen  at  900°  C.,  while  the  writer  found  the 
reverse  to  be  the  case  at  much  higher  temperatures.  Also, 
Richardson  found  Q  for  nitrogen  much  greater  than  for  oxygen, 
so  that  although  in  his  experiments  at  about  800°  C.  oxygen  gave 
the  greater  current,  it  is  clear  that  at  higher  temperatures  the 
current  in  oxygen  should  be  very  small  compared  with  that  in 
nitrogen. 

IF 

The  equation          i  —  --^  —  (vide  supra), 

'  + 


since  \  is  inversely  proportional  to  the  gas  pressure,  shows  that 
the  electric  force  required  to  make  i/I  have  a  definite  value  is 
proportional  to  the  pressure. 

Richardson1  examined  the  positive  thermionic  current  in 
hydrogen,  and  found  that  at  800°  C.  it  was  54  x  10  ~12  ampere 
on  first  letting  in  hydrogen  to  27'5  mms.  pressure,  but  fell  oft' 
after  five  hours'  heating  to  only  2'1  x  10  ~12  ampere. 

If  we  calculate  Q  from  the  current  at  1300°  C.,  and  9  mms. 
pressure,  given  above,  and  Richardson's  final  value  at  800°  C., 
we  get  Q  =  50,000,  which  is  of  the  right  order  of  magnitude.  At 
high  temperatures  the  time  required  for  the  wire  to  get  into  a 
steady  state  is  very  much  shorter  than  at  low  temperatures,  so 
that  in  my  experiments  at  1300°  C.  the  variation  did  not  last 
more  than  a  few  minutes.  Richardson  found  Q  for  the  positive 
thermionic  current  in  hydrogen  at  1'9  mms.  to  be  35,800,  and  at 
226  mms.  57,000.  These  values  are  probably  greater  than  those 
in  oxygen,  so  that  at  high  temperatures  the  positive  thermionic 
current  in  hydrogen  may  be  much  greater  than  in  oxygen, 
although  at  800°  C.  Richardson  found  it  not  more  than  one- 
twentieth  as  great. 

O.  W.  Richardson  (loc.  cit.)  also  examined  the  permanent 
positive  thermionic  current  from  platinum  in  several  other  gases. 

1  Phil.  Trans.  A.  vol.  207,  p.  1,  1906. 


DISCHARGE   OF   POSITIVE   ELECTRICITY        51 

He  found  that  the  current  (i)  from  platinum    at  730°   C.  and 
820°  C.  in  oxygen  could  be  represented  by  the  equation — 


i          •     j. 

where  p  denotes  the  pressure  and  a  and  ft  are  constants.     The 
following  table  is  taken  from  his  paper: — 


Pressure 
in  mms.  of  Hg. 

i 
(calculated). 

i 
(observed). 

1  =  10  -12  ampere 

0-003 

0-75 

1-0 

0-17 

5-2 

5-9 

1-5 

13-2 

15 

3-1 

17-1 

17 

10-7 

25 

23-5 

30 

32-3 

30 

97 

39-5 

38 

200 

437 

43 

399 

467 

49-3 

587 

48:3 

50-5 

766 

49 

53-5 

These  numbers  are  for  a  wire  at  820°  C.  The  calculated 
values  were  got  by  taking  a  =  56  and  ft  =  4.  When  p  is  large, 
the  current  becomes  nearly  independent  of  p,  and  at  820°  C.  its 
maximum  value  is  2'5  x  10  ~10  amperes  per  sq.  cm. 

At  1170°  C.  the  currents  agreed  well  with  the  equation  — 


where  a  =  38  x  10 -10  ampere,  and  ft  =  4'8  mms.  of  Hg.  It 
appears,  therefore,  that  when  p  is  small  i  varies  as  pn  and  that 
n  increases  considerably  with  the  temperature. 

Richardson  explained  the  relation  between  i  and  p  by  the 
theory  referred  to  on  page  38. 

The  variation  of  the  positive  thermionic  current  with  the 
temperature  at  constant  pressure  appears  to  agree  in  all  cases 
with  the  formula  i  =  A0*e-Q/2*,  so  that  just  as  with  the  negative 
current  in  hydrogen,  A  and  Q  must  be  functions  of  the  pressure, 
such  as  are  consistent  with 


-;- 
P+pn 

where  A  and  Q  depend  only  on  p  and  a,  ft  and 


only  on  0. 


E  2 


52 


ELECTRICAL   PROPERTIES   OF  FLAMES 


The  data  available,  however,  are  not  sufficient  to  test  this 
conclusion.  Since  n  increases  with  the  temperature,  we  should 
expect  Q  to  increase  with  the  pressure.  In  oxygen  at  2  mms. 
pressure  Richardson  found  Q  =  3  x  104  and  in  air  at  760  mms. 
Q  =  4*9  x  104.  In  hydrogen,  also,  as  we  have  seen,  Q  for  positive 
currents  increases  with  the  pressure. 

Richardson  also  examined  the  positive  thermionic  current 
in  nitrogen  and  helium.  It  increased  with  pressure  in  each  case. 
At  about  900°  C.  the  current  in  nitrogen  was  about  one-tenth 
that  in  oxygen,  while  in  helium  it  was  about  one-third  that  in 
oxygen. 

Richardson  gives  the  following  table  of  values  of  Q : — 


Gas. 

Pressure,  mms. 

Q  for  +  ions. 

Qfor 

-  ions. 

02 

2 

3-04  x  104 

13-55 

x  104 

Air 

760 

4-92     „ 

8-97 

11 

^2 

2-8 

7-12     „ 

11-2 

11 

H2 

1-9 

3-58     „ 

12-0 

11 

H2 

226 

5'7       „ 

5-56 

11 

According  to  these  numbers  the  ratio  of  the  positive  current 

-4-08          -JQ4 

in  nitrogen  to  that  in  oxygen  is  proportional  to  s  20  so 

that  at  high  temperatures  the  current  in  oxygen  should  be  negli- 
gible compared  with  the  current  in  nitrogen.  A  series  of  determi- 
nations of  the  values  of  A  and  Q  for  platinum  in  oxygen  and 
other  gases  at  all  pressures  from  0  to  760  mms.  would  prob- 
ably throw  much  light  on  the  process  of  formation  of  the 
positive  ions. 

Richardson  (loc.  cit.)  found  that  when  the  temperature  or 
pressure  is  changed,  the  positive  thermionic  current  in  oxygen 
lags  behind,  showing  that  time  is  required  for  the  platinum  to  get 
into  equilibrium  with  the  oxygen,  just  as  with  the  negative  current 
in  hydrogen. 

It  will  be  observed  that  there  is  a  close  analogy  between  the 

,    negative  thermionic  current  in  hydrogen  and  the  positive  current 

in  different  gases.     Both  appear  to  be  due  to  the  presence  of  the 

gas  in  the  surface  layer  of  the  hot  solid,  but  the  precise  nature 

of  the  action  is  unknown.     The  fact  that  the  current  increases 


DISCHARGE   OF   POSITIVE   ELECTRICITY        53 

regularly  with  the  pressure  at  low  pressures  suggests  that  the  gas 
dissolves  in  the  platinum  without  forming  a  definite  compound, 
for  if  a  definite  compound  were  formed,  we  should  expect  com- 
plete combination  above  its  dissociation  pressure,  and  complete 
decomposition  below  it.  At  higher  pressures,  since  the  leak 
becomes  nearly  independent  of  the  pressure,  chemical  com- 
bination is  suggested. 

Sir  J.  J.  Thomson1  found  that  many  salts  when  heated  gave  a 
large  thermionic  current.  Phosphates  of  Al,  Fe,  Hg,  Ca,  Zn,  Pb, 
Ag,  Sn,  all  gave  positive  currents.  With  Al,  Fe,  and  Hg 
phosphates  the  current  was  very  large.  Nitrates  and  chlorides 
also  gave  positive  currents.  Oxides  gave  an  excess  of  negative 
ions,  especially  the  alkaline  earths. 

Sir  J.  J.  Thomson  (loc.  cit.)  made  the  interesting  discovery  that 
when  the  same  compounds  were  powdered  in  a  mortar  they 
acquired  a  charge  of  the  opposite  sign  to  that  which  they  evolved 
on  heating ;  the  mortar  and  pestle,  of  course,  got  a  charge  of  the 
opposite  sign  to  the  compound. 

Sir  J.  J.  Thomson  suggested  that  the  compounds  are  covered 
with  an  electrical  double  layer,  and  that  those  which,  like  alumin- 
ium phosphate,  evolve  positive  ions  when  heated  and  become 
negative  when  rubbed,  have  the  positive  charge  in  the  layer  on  the 
outside.  The  oxides,  he  suggested,  have  the  negative  charge  on  the 
outside,  and  rubbing  or  heating  removes  some  of  the  outside  layer. 
The  layers,  of  course,  may  contain  molecules  of  the  surrounding 
gas.  On  this  view,  the  escape  of  the  ions  at  high  temperatures  is  a 
kind  of  evaporation. 

Garrett  2  determined  e/m  for  the  ions  emitted  by  aluminium 
phosphate.  He  found  10  per  cent,  of  the  ions  had  e/m  =  9700,  which 
shows  that  they  were  probably  hydrogen  atoms.  He  found  that 
when  the  phosphate  is  moistened  with  water  the  production  of 
ions  is  greatly  increased  until  the  -water  is  all  driven  off  by 
heating. 

F.  Horton3  examined  the  spectrum  of  the  gas  evolved  by  a 
platinum  strip  coated  with  aluminium  phosphate,  when  it  was 

.    l  Proc.  Camb.  Phil.  Soc.  vol.  xiv.  p.  105,  1907. 

2  Phil  Mag.,  October  1910. 

3  Proc.  Roy.  Soc.  A.  vol.  84,  p.  433,  1910. 


54         ELECTRICAL  PROPERTIES   OF   FLAMES 

heated   strongly   in   a   vacuum.      This   substance  was  found   by 
Sir  J.  J.  Thomson  to  give  a  large  positive  thermionic  current. 

Horton  found  that  the  spectra  of  oxygen  and  carbon  were 
always  present,  and  concluded  that  the  carriers  of  the  thermionic 
current  were  carbon  monoxide  molecules.  It  is  well  known  that 
carbon  monoxide  is  very  often  present  in  vacuum  tubes,  especially 
in  the  presence  of  considerable  masses  of  metal,  which  always 
evolve  CO  when  put  in  a  vacuum.  In  Richardson's  experiments 
on  e/m  for  the  positive  ions  emitted  by  various  metals,  CO  was, 
no  doubt,  present,  so  that  it  seems  possible  that  some  of  the 
carriers  may  have  been  CO. 

In  Sir  J.  J.  Thomson's  experiments  the  aluminium  phosphate 
emitted  a  copious  supply  of  positive  ions  when  heated  in  air  at 
atmospheric  pressure.  In  this  case  there  could  not  have  been 
any  CO  present,  so  that  it  is  clear  that  the  positive  ions  are  not 
always  CO.  They  are  probably  formed  from  any  substance 
present,  and  a  constituent  of  the  salt  seems  much  the  most 
probable. 

Horton l  examined  the  thermionic  current  from  hot  platinum 
coated  with  sodium  phosphate.  At  800°  C.  in  oxygen  and  CO  he 
found  it  increased  with  the  pressure  up  to  about  3  mms.  of 
mercury  and  then  diminished  about  25  per  cent,  from  3  mms.  to 
8  mms.  The  positive  thermionic  current  in  oxygen  at  800°  C.  was 
about  ten  times  smaller  than  in  carbon  monoxide.  In  hydrogen  at 
800°  C.  the  positive  thermionic  current  did  not  diminish  with  the 
pressure  above  3  mm.,  but  remained  nearly  constant.  It  was 
about  ten  times  larger  in  hydrogen  than  in  carbon  monoxide.  As 
already  mentioned,  the  relative  values  of  the  currents  in  different 
gases  depend  very  greatly  on  the  temperature,  since  Q  depends  on 
the  nature  of  the  gas  and  on  its  pressure. 

Horton  found  that  the  current  in  oxygen  diminished  with  long- 
continued  heating,  whereas  in  CO  it  increased  rapidly  on  first 
admitting  the  gas.  These  results,  on  the  whole,  support  the  view 
that  the  carriers  are  CO  molecules  in  some  cases.2  With  clean 
platinum  in  pure  hydrogen  they  are  no  doubt  hydrogen  atoms,  or 

1  Proc.  Cam.  Phil.  Soc.  vol.  xvi.  p.  89,  1910. 

2  Davisson  Hnds  that  the  positive  ions  from  salts  are  not  molecules  of  the 
gases  present. — Phil.  Mag.,  January  1912. 


DISCHARGE   OF   POSITIVE   ELECTRICITY         55 

molecules,  and  in  pure  oxygen,  oxygen  atoms,  or  molecules.     If 
any  sodium  is  present  it  no  doubt  helps  to  supply  the  carriers. 

Platinum  and  most  other  substances  disintegrate  or  splutter  to 
a  greater  or  less1  extent  when  heated  to  a  high  temperature  in 
gas  at  low  pressure.  This  effect  depends  greatly  on  the  nature  of 
the  gas.  It  is  greater  with  platinum  in  oxygen  than  in  nitrogen 
or  hydrogen. 

When  the  hot  body  is  spluttering,  some  of  the  thermions  get 
attached  to  the  minute  particles  coming  off,  and  so  become  very 
large  ions,  which  have  a  very  small  velocity  due  to  an  electric 
field.  " 

The  fact  that  the  spluttering  depends  on  the  gas  suggests  that 
it  may  be  connected  with  the  formation  and  decomposition  of 
unstable  compounds  at  the  surface  of  the  hot  body. 

The  spluttering  o(  the  cathodes  in  vacuum  tubes  is  very  analo- 
gous to  the  spluttering  of  hot  bodies.  It  also  depends  on  the  gas  ; 
for  example,  aluminium  does  not  splutter  in  ordinary  gases,  but 
does  in  helium,  argon,  and  other  monatomic  gases.  Since  helium 
and  argon  do  not  combine  chemically  with  other  elements,  this 
seems  to  show  that  the  spluttering  of  cathodes  is  not  connected 
with  ordinary  chemical  action. 

The  positive  thermionic  current  from  platinum  in  hydrogen  or 
nitrogen  at  high  temperatures  is  greater  than  in  oxygen,  but  the 
spluttering  is  greater  in  oxygen  than  in  hydrogen. 

G.  Owen1  made  a  series  of  experiments  on  the  nuclei  for  cloudy 
condensation  emitted  by  a  hot  platinum  wire  in  air,  and  in 
hydrogen.  He  found  these  nuclei  were  unaffected  by  an  electric 
field.  They  are  probably  molecules  of  platinum,  and  are  bigger, 
he  found,  the  higher  the  temperature. 

If  the  dust  given  off  by  hot  platinum  in  air  is  allowed  to 
accumulate  in  the  air  near  the  platinum,  many  of  the  ions  emitted 
get  attached  to  dust  particles,  which  may  make  it  impossible  to 
saturate  the  current,  even  when  the  electrodes  are  near  together. 
This  can  be  prevented  by  passing  a  .  rapid  current  of  air  between 
the  electrodes,  so  as  to  blow  out  the  dust  particles,  as  was 
done  in  my  experiments  described  at  the  beginning  of  this 
chapter. 

1  Phil.  Mag.,  September  1903. 


56         ELECTRICAL  PROPERTIES   OF  FLAMES 

So  far  as  can  be  judged  at  present,  there  does  not  seem  to  be 
any  very  intimate  connection  between  the  disintegration  of 
platinum  and  the  thermionic  current  from  it. 

Beattie  found  that  various  mixtures  of  substances  when 
heated  to  between  300°  C.  and  400°  C.  emit  ions  which  are  usually 
mostly  positive.  For  example,  a  mixture  of  sodium  chloride  and 
i  odine  on  a  zinc  plate  gives  a  copious  supply  of  positive  ions  at 
350°  C. 

Garrett  and  Willows  found  that  zinc  chloride,  bromide  and 
iodide  give  off  positive  ions  when  heated  to  a  few  hundred  degrees. 
They  found  the  velocity  of  the  ions  emitted  to  be  about  0.060  cms. 
per  sec.  for  one  volt  per  cm.  in  air  at  atmospheric  pressure. 
These  ions  produce  a  cloud  when  passed  over  water.  Garrett  in  a 
further  investigation  concluded  that  the  production  of  these 
positive  ions  is  due  to  chemical  action  and  is  similar  to  the 
production  of  the  ions  found  in  newly  prepared  gases  and  in  the 
fumes  from  phosphorus.  It  therefore  falls  outside  the  province  of 
this  book. 


CHAPTER   VI 
THE  CONDUCTIVITY  OF  THE   BUNSEN   FLAME 

A  BUNSEN  coal-gas  flame  is  a  good  conductor  of  electricity. 
If  two  platinum  electrodes  are  placed  in  such  a  flame,  so  that 
they  get  red  hot,  and  are  connected  to  a  battery,  the  current 
between  them  can  be  easily  measured  with  a  galvanometer. 
Fig.  7  shows  a  convenient  apparatus  for  experiments  of  this 
kind. 

A  brass  tube  AB,  about  5  cms.  in  diameter  and  70  cms.  long, 
is  mounted  horizontally  on  a  wooden  stand,  as  shown.  The  end 
B  is  closed  with  a  cork,  while  at  A  a  gas  jet  is  fixed  so  as  to  send 


FIG.  7. 

a  stream  of  coal  gas  down  the  tube.  Twenty-five  small  brass  tubes, 
each  about  6  mms.  in  diameter  and  15  mms.  long,  are  soldered 
into  a  row  of  holes  1  cm.  apart  along  the  upper  surface  of  the 
large  tube,  near  the  end  B.  To  each  of  these  a  fused  quartz  tube 
about  3  cms.  long  is  attached  with  a  short  piece  of  indiarubber 
tubing.  The  quartz  tubes  should  all  be  as  nearly  as  possible 
equal  and  of  the  same  internal  diameter  as  the  small  brass  tubes. 
This  arrangement  will  act  like  a  Bunsen  burner,  and  gives  a  flame 
about  26  cms.  long  and  7  cms.  high.  The  jet  at  A  should  be 
supported  so  that  its  distance  down  the  tube  can  be  adjusted 
and  the  diameter  of  the  jet  be  so  chosen  as  to  give  a  non-luminous 

57 


58         ELECTRICAL  PROPERTIES    OF   FLAMES 

flame  with  a  well-defined  inner  cone  on  each  quartz  tube.  A 
jet  about  2  mms.  in  diameter  will  probably  be  nearly  right. 

Two  vertical  platinum  discs  E,  E,  about  1'5  cms.  in  diameter, 
made  of  thick  foil,  welded  to  platinum  wires  about  1  mm.  thick, 
form,  convenient  electrodes.  The  wires  can  be  fused  into  glass 
tubes  and  supported  on  small  adjustable  stands  SS,  as  shown. 
One  of  the  electrodes  may  be  supported  near  one  end  of  the 
flame,  and  the  stand  for  the  other  made  to  slide  in  a  groove 
parallel  to  the  flame,  so  that  the  electrodes  can  be  easily  placed 
at  any  distance  apart.  The  platinum  wires  should  be  long  enough 
to  prevent  the  ends  of  the  glass  tubes  getting  too  hot. 

The  following  table  gives  the  currents  observed l  with  such 
an  apparatus  (1  =  8*8  x  10~9  ampere):— 


Distance  between  Electrodes. 

Potential 

-  Difference. 

1  cm. 

4-5  cm. 

9  cm. 

13-5  cm. 

18  cm. 

600  volts 

/ 

310 

304 

295 

280 

270 

400 

255 

247 

240 

230 

215 

200   " 

175 

170 

165 

.155 

143 

120 

130 

125 

115 

104 

90 

40 

67 

64 

57 

53 

48 

20 

42 

39 

35 

32 

29 

10 

22 

20 

16 

14 

13 

4 

9 

8 

7 

6 

5'3 

2 

5 

4-7 

4 

3  '5 

3 

It  will  be  seen  that  in  every  case  the  current  falls  off  slowly 
with  increasing  distance  between  the  electrodes.  When  the 
distance  between  the  electrodes  is  small  the  current  (C)  is  nearly 
proportional  to  the  square  root  of  the  potential  difference  (V), 
provided  this  is  greater  than  three  or  four  volts.  Fig.  8  shows 
the  relation  between  the  current  and  potential  for  two  electrodes 
1  cm.  apart  in  an  ordinary  Bunsen  flame.  One  of  the  electrodes 
was  a  platinum  disc  3  cms.  in  diameter,  and  the  other  a  disc  1  cm. 
in  diameter,  surrounded  by  a  guard  ring  3  cms.  in  diameter.  The 
curve  drawn  is  the  parabola  C  =  19'25^/V. 

If  one  of  the  electrodes  is  moved  so  near  the  edge  of  the  flame 


H.  A.  Wilson,  Phil.  Mag.,  October  1905. 


CONDUCTIVITY   OF   THE   BUNSEN   FLAME        59 

that   it   becomes   less   hotk   the   current    is   greatly   diminished, 
especially  if  the  cooler  electrode  is  negative. 

The  conductivity  of  an  ordinary  Bnnsen  flame  can  be  measured    ,j 


40  VOLTS 


between  horizontal  electrodes  one  above  the  ott^er,  consisting  of 
platinum  wire  gauze.  The  gauze  should  not  have  more  than 
three  or  four  wires  per  centimetre,  so  that  the  flame  can  'pass 
freely  through  it. 


250 


HO     160      Ted     eoocetts. 
(too  cell*  •  &6o  rol,te>. 


FIG.  9. 


Fig.  9  shows  the  relation  "between  the  current  and  P.D. 
obtained  in  this  way,1  the  lower  electrode  being  negatively 
charged  and  about  2  cms.  above  the  burner. 

1  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  192,  p.  499,  1899. 


60 


ELECTRICAL  PROPERTIES    OF   FLAMES 


Fig.  10  shows  the  relation  between  the  current  and  distance 
between  the  gauze  electrodes. 

The  current  was  almost  independent  of  distance  up  to  3  cms. 
but  then  fell  off  rapidly.  This  was  mainly  due  to  the  upper 
electrode  getting  cooler  when  near  the  top  of  the  flame.  If  the 
upper  electrode  was  kept  at  a  nearly  constant  temperature,  by 
passing  a  current  through  -it,  the  current  was  nearly  independent 
of  the  distance,  right  up  to  the  top  of  the  flame.  With  horizontal 
gauze  electrodes  the  current  of  gas  carries  up  a  continuous  large 
supply  of  ions  between  the  electrodes  from  below  them,  so  that 
we  should  expect  a  large  current  to  be  obtained,  even  with  the 
electrodes  very  close  together. 


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1           ^          3           4          5          6           7          d          9  Cms. 

FIG.  10. 

The  variation  of  the  potential  along  the  flame  from  one 
electrode  to  the  other  was  examined 1  by  means  of  a  fine  platinum 
exploring  wire,  connected  to  an  electrostatic  voltmeter  or  quadrant 
electrometer.  The  voltmeter  was  connected  to  one  of  the  electrodes 
and  to  the  wire.  The  wire  was  perpendicular  to  the  line  joining 
the  electrodes,  and  could  be  moved  along  the  flame  from  one 
electrode  to  the  other.  Since  the  flame  is  a  conductor  and  the 
wire  insulated,  it  takes  up  the  potential  of  the  flame  at  the  place 
where  it  is  put  in. 

Fig.  11  shows  the  variation  of  the  potential  obtained  in  this 


1  H.    A.   Wilson,  Phil.   Trans.  A.  vol.    192,  p.,  499,  1899  ;   Phil.  Mag., 
October  1905.     Marx,  Ann.  der  Phys.  vol.  iv.  p.  2,  1900. 


CONDUCTIVITY   OF   THE   BUNSEN  FLAME       61 


way  with  the  electrodes  17'7  cms.  apart,  and  a  P.D.  of  550  volts, 
between  them. 

It  will  be  seen  that  there  is  a  uniform  potential  gradient 
except  near  to  the  electrodes.  Near  the  negative  electrode  there 
is  a  large  fall  of  potential,  and  a  small  one  close  to  the  positive 
electrode.  Such  a  variation  of  the  potential  is  characteristic  of 
conduction  through  flames,  and  always  occurs  when  both  the 
electrodes  are  hot.  If  one  of  the  electrodes  is  moved  near  to  the 
edge  of  the  flame,  so  that  it  becomes  cooler,  the  fall  of  potential 
near  it  increases.  In  this  way  nearly  all  the  drop  of  potential 
can  be  concentrated  at  either  the  positive  or  negative  electrode. 


400 


200 


8        '0 
FIG.  11. 


12 


14- 


16 


1 8  CMS. 


The  uniform  gradient  between  the  electrodes  is  proportional 
to  the  current.  This  was  shown  by  using  two  exploring  wires, 
kept  at  a  constant  distance  apart  and  connected  to  an  insulated 
quadrant  electrometer.  The  following  numbers  were  obtained 
in  this  way.1 


Current  (C) 
1  =  S-s  x  10  -9  ampere. 

P.D.  between 
exploring  wires. 

P.D.  -=-  c. 

270 
54 
18 

4-0  volts 

0-8     „ 
0'25  „ 

0-015 
0-015 
0-014 

The  exploring  wires  were  O5  cm,  apart. 

H.  A.  Wilson,  Phil,  Mag.,  October  1905. 


62         ELECTRICAL   PROPERTIES   OF   FLAMES 

Mr.  E.  Gold1  found  the  uniform  gradient  proportional  to  the 
current  between  the  limits  5  x  10  ~6  ampere  and  260  X  10  ~6 
ampere.  In  his  experiments  the  current  was  increased  by  putting 
alkali  salts,  such  as  potassium  carbonate,  on  the  negative  electrode, 
but  the  salt  vapour  did  not  extend  into  the  part  of  the  flame 
where  the  exploring  wires  were  put  in.  It  appears,  therefore, 
that  at  a  distance  from  the  electrodes  the  flame  obeys  Ohm's 
law.  In  Mr.  E.  Gold's  experiments,  the  ratio  of  the  potential 
gradient  in  volts  per  centimetre  to  the  current  in  amperes  was 
0'70  x  105.  The  cross-section  of  the  flame  was  about  2  sq.  cms., 
so  that  the  specific  resistance  of  the  flame  was  1'4  x  105  ohms 
per  c.c.  In  my  experiments  just  mentioned  the  specific  resist- 
ance was  about  2  x  106  ohms  per  c.c.  The  specific  resistance  of  a 
Bunsen  flame  varies  greatly  with  the  composition  of  the  mixture 
of  coal  gas  and  air. 

The  fall  of  potential  in  the  uniform  gradient  between  the 
electrodes  is  equal  to  Acd,  where  c  is  the  current,  d  the  distance 
between  the  electrodes,  and  A  a  constant.  When  d  is  small, 
Acd  can  be  neglected  compared  with  the  total  fall  of  potential  (V), 
and  then  V  =  Be2  approximately,  as  we  have  seen.  In  any  case, 
therefore,  the  equation  — 

V  =  Acd  +  Be2 

represents  the  relation  between  the  current,  potential  difference, 
and  distance  between  the  electrodes.  The  numbers  given  in  the 
table  supra  are  represented  approximately  by  this  equation  with 
A  =  0'03  and  B  =  0-0061.  The  term  Be2  is  equal  to  the  fall  of 
potential  near  the  electrodes. 

If  H!  denotes  the  number  of  positive  ions  per  c.c.  in  the  flame, 
€x  the  charge  on  each  ion,  t^  the  velocity  with  which  they  are 
moving  in  the  direction  from  one  electrode  to  the  other,  and  n2, 
£2  and  vz  denote  the  corresponding  quantities  for  the  negative  ions, 
then  the  current  per  sq.  cm.  (i)  is  given  by  the  equation  — 


The  velocity  of  an  ion  through  a  gas  is  proportional  to  the 
strength  of  the  electrical  field  (X),  so  that  if  the  gas  is  flowing 

1  Proc.  Roy.  Soc.  A.  vol.  79,  1907. 


CONDUCTIVITY   OF   THE   BUNSEN   FLAME       63 

towards  the  negative  electrode  with  velocity  u,  we  have 

l\  =  ^i-^-  ~^~  u 

V,2  =  £2X  -  U 

where  7^  and  &2  denote  the  velocities  of  the  ions  relative  to  the 

gas  in  unit  field. 

Hence  —  i  =  ?i1e1(7t1X  +  u)  +  ^2  (^2-^-  ~~  u\ 

Take  the  axis  of  x  perpendicular  to  the  surfaces  of  the 
electrodes,  and  suppose  that  everything  is  constant  over  planes 
parallel,  to  the  electrodes,  then 


/ 

In   the   uniform   gradient    between    the   electrodes   -,  -  =  0, 
so  that  n^  =  nzez,  and  therefore 


and  is  therefore  independent  of  the  velocity  of  the  flame  gases. 
Comparing  this  with  the  equation  V  =  Adc  -f  Be2,  we  see  that 

•      y  x  =  yAa  =  ^to  +*i>     •"   . 

where  a  is  the  cross-section  of  the  flame. 

Thus,  the  fact  that  the  flame  at  a  distance  from  the  electrodes 
obeys  Ohm's  law,  shows  that  the  velocities  of  the  ions  in  it  are 
proportional  to  the  strength  of  the  electric  field. 

The  theory  of  the  relation  between  the  current  and  the 
potential  difference  in  an  ionized  gas  is  given  by  Sir  J.  J.  Thomson 
in  his  book  on  The  Conduction  of  Electricity  through  Gases, 
chap,  iii,  and  I  shall  only  give  here  a  short  discussion  of  some 
points  which  apply  particularly  to  conduction  through  flames. 

In  nearly  all  cases  of  the  conduction  of  electricity  through 
gases  the  charge  on  a  positive  ion  is  equal  to  the  charge  on  a 
negative  ion.  If  we  assume  that  this  is  the  case  in  flames,  we 
obtain 

_  =  ^(X  -  n2)e      .     .....     (1) 


and  en^kJL  +  u)  +  en2(k2X  —  u)  =  i   .....     (2) 

where  u  is  the  velocity  of  the  gas  in  the  direction  of  x. 


64         ELECTRICAL  PROPERTIES   OF  FLAMES 

These  equations  give 
1 


~ 


Let  the  positive  electrode  be  at  #  =  0  and  the  negative  at 
x  =  1.  In  the  case  where  u  =  0  close  to  the  positive  electrode  we 
have  ?ix  =  0,  because  the  positive  ions  all  move  towards  the  negative 
electrode,  while  at  the  negative  electrode  nz  =  0.  Hence,  from 
(3)  and  (4),  in  this  case  — 


. 
=       8m 

dx  Jx  = 


(5) 


These  equations  enable  &x  and  kz  to  be  easily  calculated  from  tire 
variation  of  X  near  the  electrodes  ;  but  only  rough  estimates  can 
be  got  in  this  way,  because  it  is  impossible  to  measure  X  very 
exactly  close  to  the  electrodes. 

The  corresponding  equations  when  u  is  not  zero  can,  of  course, 
be  easily  obtained,  but  are  of  no  value. 

If  the  electrodes  are  made  of  horizontal  wire  gratings  to  allow 
the  flame  to  flow  through  them,  it  is  evident  that  u  is  not  zero, 
and  also  that  n^  and  nz  cannot  be  put  equal  to  zero  at  the  positive 
and  negative  electrodes,  respectively,  because  the  flame  gases 
contain  ions  which  are  carried  through  such  electrodes.  The 
distribution  of  electric  force  near  such  electrodes  will  not  be  the 
same  as  near  plane  electrodes,  except  at  distances  from  them 
greater  than  the  distance  between  the  wires  forming  the  grating. 
Thus,  the  equations  (5)  ought  not  to  be  applied  to  results  obtained 
with  grating  electrodes. 

In  flames  when  both  electrodes  are  hot  the  variation  of  the 
electric  -force  is  much  larger  near  the  negative  than  near  the 
positive  electrode.  This  is  shown  clearly  in  Fig.  11.  The  equa- 
tions (5)  show  that  this  means  that  the  velocity  of  the  negative 
ions  is  much  larger  than  the  velocity  of  the  positive  ions.1 

Close  to  the  negative  electrode  the  current  must  be  carried  by 

1  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  192,  p.  499,  1899. 


CONDUCTIVITY   OF  THE   BUNSEN  FLAME       65 

the  positive  ions,  so  that  the  electric  force  is  large  there,  owing  to 
the  small  velocity  of  these  ions.  At  the  positive  electrode  the 
current  is  carried  by  negative  ions  having  a  high  velocity,  so  that 
the  force  there  is  only  slightly  greater  than  in  the  uniform 
gradient. 

The  variation  of  the  potential  shown  in  Fig.  1  1  is  represented 
fairly  well,  except  close  to  the  positive  electrode,  by  the 
equation  — 

y  =  540  -  4-44^  -  462e  - 


Using  this  equation  to  calculate    (  —  —  )          we   get    by  (5) 

\  doc  /  x  —  i 

&]_  =  14  cms.  per  sec.  for  one  volt  per  cm.,  which,  of  course,  is 
subject  to  a  large  possible  error.  This  appears  to  be  the  only 
estimate  yet  made  of  the  velocity  of  the  positive  ions  in  a  Bunsen 
flame  free  from  salt  vapours.  The  gases  present  in  such  a  flame 
are  N2,  H2O,  CO,  CO2,  etc.  An  ion  consisting  of  OO2  would  prob- 
ably have  a  velocity  of  about  40  cms.  per  sec.,1  which  is  of  the 
same  order  as  that  just  found.  There  seems,  therefore,  no  reason 
to  doubt  that  the  positive  ions  in  a  Bunsen  flame  free  from  salt 
consist  simply  of  charged  molecules  of  the  gases  present. 

The  variation  of  the  potential  gradient  near  the  positive 
electrode  is  too  slight  to  enable  kz  to  be  estimated  in  this  way,  but 
it  is  clear  that  it  must  be  of  a  much  higher  order  of  magnitude. 

Let  q  denote  the  number  of  fresh  ions  of  either  sign  produced 
per  c.c.  per  sec.,  and  consider  a  layer  of  thickness  dx  perpendicular 
to  the  x  axis.  Inside  one  sq.  cm.  of  this  layer  qdx  fresh  positive 
ions  are  produced  per  sec.,  and  an^n^dx  positive  ions  disappear  by 
recombination,  a  being  the  coefficient  of  recombination.  The 
number  of  positive  ions  entering  the  layer  due  to  the  electric  field 

is  7v1X^1,  so  that  in  a  steady  state,  when  —^-  —  0,  we  have 

(6) 


In  the  same  way  for  the  negative  ions  — 


See  p.  86. 


66         ELECTRICAL  PROPERTIES   OF  FLAMES 
(1),  (6),  and  (7)  give 


It  follows  from  (1)  and  (8)  that  in  the  uniform  potential  gradient 
between  the  electrodes,  nl  =  n2—  n  and  q  —  an.2     Hence  — 

+  kz)  =  Xc  fa  +  />'.,)  JI 


>  a 

Equation  (8)  shows  that—  ^  is  positive  when  the  ionization  q 

is  greater  than  the  recombination  a  n^n^.  In  the  layers  near  the 
electrodes  there  must  be  an  excess  of  ionization  over  recombina- 
tion, because  in  the  uniform  gradient  XQ-JI&J  positive  ions  per 
sq.  cm.  flow  past  per  sec.,  away  from  the  positive  electrode,  and 
X0'W&2  negative  ions  away  from  the  negative  electrode.  Thus 
d2X2/cfe2  must  be  positive  near  each  electrode,  so  that  the  curve 
giving  the  relation  between  X2  and  x  must  be  convex  to  the  a?  axis 
near  the  electrodes.  Consequently,  the  electric  force  rises  as 
either  electrode  is  approached.  Since  &2  is  much  greater  than  \ 
the  excess  of  ionization  over  recombination  is  much  greater  near 
the  negative  electrode  than  near  the  positive,  so  the  variation  in 
X  near  the  negative  electrode  is  much  greater  than  near  the 
positive  electrode. 

If  &2  is  very  large  compared  with  k:  then  the  current  will  be 
nearly  equal  to  Xe?i2&2  except  close  to  the  negative  electrode, 
where  n2  =  0  and  the  current  is  equal  to  'K.enfa  in  any  case.  The 
theory  of  the  distribution  of  the  electric  force  between  the 
electrodes  can  be  greatly  simplified  1  when  k2  is  large  compared 
with  &]_  by  assuming  that  the  current  is  equal  to  Xe%2&2,  but  this 
assumption  obviously  fails  close  to  the  negative  electrode. 

Equations  (3),  (4),  and  (5),  when  u  =  0,  give 

/dX*\  __  dX2 

&2?i2       \  dx  )x  =  I        dx 


\dx)x  =  0  "    dx 


Since  (-T—  )        is  nearly  zero,  we  have,  approximately, 

\  CtOC  /  x  =  0 

1  J.  J.  Thomson,  Conduction  of  Electricity  through  Gases,  chap.  iii. 


CONDUCTIVITY   OF   THE    BUNSEN  FLAME       67 

kzn2  _  \  dx,  Jx  =  I 

~dx 

With  V  =  540  —  4'44a;  —  462g- 1-87('  "  *>  this  gives  the  follow- 
ing numbers — 

0  cms.  0 

01  „  0-45 
0-5     „  5-3 
1-0     „                              39 

It  appears,  therefore,  that  in  the  case  shown  in  Fig.  11  the 
current  carried  by  the  positive  ions  is  half  the  total  current  one 
millimetre  from  the  negative  electrode,  and  one-fifth  five  milli- 
metres from  it,  but  at  one  cm.  away  it  is  only  3  per  cent.  Most 
of  the  fall  of  potential  occurs  within  one  cm.  of  the  negative 
electrode,  so  that  it  is  clear  that  the  variation  of  the  potential 
near  the  negative  electrode  cannot  be  accurately  calculated  by 
assuming  that  i  =  X.enjc2.  J.  J.  Thomson  *•  found  that  the  varia- 
tion of  the  potential'  near  the  negative  electrode,  calculated  on 
the  assumption  that  i  =  Jienjtzt  does  not  agree  with  that  observed. 

We  have  seen  that  near  the  negative  electrode  the  excess  of 
ionization  over  recombination  is  equal  to  kznK0,  where  n  is  the 
number  of  negative  or  positive  ions  per  c.c.  in  the  uniform  gradient, 
and  X0  the  electric  force  there.  This  number  of  negative  ions  is 
produced  per  sec.  in  a  layer  next  to  the  negative  electrode  of 
thickness  12,  where  ql%  —  kz'iiK0. 

If,  following  J.  J.  Thomson,  we  assume  that  in  this  layer  no 
recombination  takes  place,  and  that  outside  it  the  electric  force  is 
uniform  and  equal  to  X0,  then  the  fall  of  potential  in  the  layer  can 
be  calculated.  It  comes  out  proportional  to  i2.  Near  the  positive 

electrode  we  may  imagine  a  similar  layer  of  thickness  ^  =  -• 

in  which  also  the  drop  of  potential  is  proportional  to  i2.  In  the 
uniform  gradient  the  fall  of  potential  is  proportional  to  the  current 
and  to  the  distance  between  the  electrodes,  so  that  V  =  Ale  +  Be2, 


p  2 


1  Conduction  of  Electricity  through  Gases,  p.  235,  1906. 


68 


ELECTRICAL   PROPERTIES   OF  FLAMES 


which  is.  the  equation  which  we  have  seen  represents  the 
experimental  results  satisfactorily. 

The  ratio  of  /x  to  A2  is  equal  to  kjky 

In  the  curve  shown  in  Fig.  11  the  potential  gradient  is 
uniform  up  to  about  2  cms.  from  the  cathode,  and  less  than  1  mm. 
from  the  anode.  If  we  suppose  these  distances  to  represent  A., 
and  Aj  we  see  that  &2  must  be  at  least  twenty  times  kr  This 
method  of  estimating  kjk^  was  used  by  Marx.1  It  is  clearly  too 
inaccurate  to  have  any  value  for  the  assumption  that  recombina- 
tion does  not  take  place  inside  the  layers  cannot  be  true  in  flames, 
and  the  width  of  the  layers  cannot  be  estimated  at  all  accurately. 


FIG.  12. 

Inside  the  Bunsen  flame  the  fall  of  potential  between  the 
electrodes  always  consists  of  large  drops  near  the  electrodes,  with 
a  small  gradient  between.  If  one  of  the  electrodes  is  much  colder 
than  the  other,  the  greater  drop  takes  place  at  the  colder  electrode, 
whether  it  is  positive  or  negative.  Fig.  12,  given  by  Marx,2  shows 
how  the  shape  of  the  potential  curves  for  two  horizontal  electrodes 
depends  on  the  temperature  of  the  positive  electrode.  Its 
temperature  was  altered  by  raising  the  electrodes  in  the  flame, 
keeping  the  distance  between  them  constant. 

1  Loc.  cit.  *  Loc.  cit. 


CONDUCTIVITY   OF   THE    BUNSEN   FLAME       69 

In  the  uniform  gradient  q  =  an2,  so  that  none  of  the  ionization 
there  contributes  to  the  current.  It  is  clear,  therefore,  that  the 
current  is  always  far  from  saturation  when  there  is  a  uniform 
gradient  in  the  middle  and  sudden  drops  of  potential  near  the 
electrodes.  On  the  layer  theory  (Ax  -f-  A2)/7  is  the  ratio  of  the 
actual  current  to  saturation  current. 

The  current  between  the  two  hot  parallel  plates  in  the  flame 
does  not  diminish  appreciably,  even  when  the  distance  between 
them  is  altered  from,  say  2  cms.  to  1  mm.,  which  shows  clearly 
that  the  current  is  very  far  from  its  saturation  value  at  the  larger 
distance.  It  would  be  interesting  to  make  experiments  on  the 
variation  of  the  current  with  the  distance  between  the  electrodes 
at  very  small  distances. 

Hot  electrodes  in  a  Bunsen  flame  must  emit  ions  which  will 
help  to  carry  the  current  at  the  surface  of  the  electrodes.  The 
fraction  of  the  current  carried  by  these  ions  is  usually  small.  It 
is  easy  to  see  that  if  the  negative  electrode  emitted  &27iX0  nega- 
tive ions  per  sec.,  the  drop  of  potential  near  that  electrode  would 
disappear,  and  the  uniform  gradient  would  extend  right  up  to  it. 
Since  this  does  not  happen,  even  when  very  small  currents  are 
passed  through  the  flame,1  it  is  clear  that  the  thermionic  current 
is  relatively  very  small. 

F.  L.  Tufts  2  found  that  coating  the  negative  electrode  with 
lime  caused  the  potential  drop  there  to  nearly  disappear.  This  is 
evidently  due  to  the  large  emission  of  negative  electrons  by  hot 
lime. 

1  E.  Gold,  Proc.  Eoy.  Sac.  A.  vol.  79,  1907. 

2  Phys.  Zeitschr.  vol.  v.  p.  76,  1904. 


CHAPTER   VII 
THE  ELECTRICAL  CONDUCTIVITY  OF  SALT    VAPOURS 


presence  of  the  vapour  of  a  metallic  salt  in  a  Bunsen 
flame  increases  its  conductivity.  Salts  of  the  alkali  metals  of 
large  atomic  weight  give  a  specially  big  effect.  This  effect  can  be 
conveniently  studied  qualitatively  with  the  apparatus  described  at 
the  beginning  of  the  last  chapter.  If  the  two  electrodes  are 
placed  about  1  cm.  apart,  and  a  bead  of  potassium  carbonate  on  a 
platinum  wire  held  below  them  so  that  the  vapour  from  it  fills  up 
the  flame  between  the  electrodes,  the  current  due  to  any  P.D.  is 
increased  probably  several  thousand  times. 

If  the  electrodes  are  placed  further  apart  the  effect  of  the  salt 
vapour  in  different  parts  of  the  space  between  the  electrodes  can 
be  easily  tried.  It  is  found  that  the  current  is  not  appreciably 
changed  unless  the  salt  vapour  is  put  in  close  to  the  negative 
electrode. 

At  the  positive  electrode,  and  anywhere  between  the  electrodes, 
there  is  no  effect,  but  if  the  salt  vapour  comes  in  contact  with 
the  negative  electrode,  a  very  large  increase  in  the  current  is 
produced. 

If  the  electrodes  are  connected  to  an  alternating  P.D.  and  some 
potassium  carbonate  placed  on  one  of  them,  a  galvanometer  in  the 
circuit  will  indicate  a  current  in  the  direction  from  the  electrode 
without  salt  to  the  other,  for  the  flame  will  practically  allow  no 
current  to  flow  in  the  opposite  direction.1 

If  salt  is  put  on  the  negative  electrode,  so  that  a  large  current 
is  obtained,  then  on  putting  in  a  bead  of  potassium  carbonate  in 
some  other  part  of  the  flame  between  the  electrodes,  it  is  found 
that  the  current  is  increased,  and  that  the  current  is  nearly 
inversely  proportional  to  the  length  of  the  flame  left  free  from  salt. 
Thus,  if  two-thirds  of  the  distance  between  the  electrodes  is 
filled  with  salt  vapour,  the  current  is  about  trebled. 

1  H.  A.  Wilson,  R.L  Lecture,  February  1909. 
70 


CONDUCTIVITY   OF  SALT  VAPOURS 


71 


With  K2CO3  on  the  negative  electrode,  the  current  diminishes 
as  the  distance  between  the  electrodes  is  increased.  This  is 
shown  in  Fig.  13.  Roughly  speaking,  the  current  is  inversely 
proportional  to  the  distance  between  the  electrodes  so  long  as  the 
positive  electrode  does  not  come  into  contact  with  the  salt  vapour 
from  the  negative  electrode. 

Coating  the  negative  electrode  with  lime  acts  in  the  same  way 
as  putting  salt  on  it,  which  was  discovered  by  Tufts 1  before  the 
similar  effect  due  to  salt  was  observed.2 


8 
FIG.   13. 


MS. 


Fig.  14  shows  the  distribution  of  potential  between  the 
electrodes  with  potassium  carbonate  on  the  negative  electrode. 

Comparing  this  with  Fig.  11,  it  will  be  seen  that  the  drop 
of  potential  at  the  negative  electrode  is  much  diminished,  and 
the  uniform  gradient  correspondingly  increased. 

If  the  two  exploring  wires  are  placed  in  the  uniform  potential 
gradient  in  the  flame,  and  connected  to  an  insulated  quadrant 
electrometer,  the  gradient,  as  we  have  seen  in  the  previous 
chapter,  is  proportional  to  the  current,  showing  that  the  flame 

1  F.  L.  Tufts,  Phys.  Zeitschr.  vol.  v.  p.  76,  1904. 
3  H.  A.  Wilson,  Phil.  Mag.,  October  1905. 


72         ELECTRICAL  PROPERTIES   OF   FLAMES 


away  from  the  electrodes,  when  free  from  salt,  obeys  Ohm's  law. 
If  a  bead  of  salt  is  put  just  below  the  two  wires,  so  that  they  are 
both  in  the  salt  vapour,  the  P.D.  between  them  becomes  practically 
zero,  although  without  salt  on  the  negative  electrode  the  current 
is  not  appreciably  affected.  This  shows  clearly  that  the  salt 
vapour  is  a  much  better  conductor  than  the  flame  by  itself. 

In  one  experiment  of  this  kind  the  principal  electrodes  were 
18  cms.  apart,  and  the  uniform  gradient,  as  indicated  by  the  explor- 
ing wires  and  electrometer,  was  1*6  volts  per  cm.  with  a  P.D.  of  700 
volts  between  the  main  electrodes.  The  current  gave  a  galvano- 
meter deflection  of  200  mms.  with  no  salt  on  the  negative 


ouu 

OLTS: 
400 

200 

< 

^ 

|S, 

^u>x^ 

* 

S^ 

"N 

<^ 

X 

\ 

\ 

— 

0 


8 
FIG. 


10 

14. 


ia 


14 


16 


electrode.  On  putting  a  bead  of  potassium  carbonate  below  the 
exploring  wires  the  electrometer  deflection  became  zero,  while  the 
current  was  unchanged.  In  the  equation 

V  =  Me  +  Be2 

the  term  Be2  represents  the  fall  of  potential  at  the  electrodes, 
and  Adc  the  fall  in  uniform  gradient.  In  this  experiment 
Adc  =  18  x  1-6  volts,  so  that  Be2  =  700  -  29  =  671  volts.  Now, 
the  salt  vapour  occupied  about  2  cms.  of  the  flame,  so  that  when 
it  was  put  in  the  fall  in  the  uniform  gradient  was  diminished  by 
2  x  1;6  =  3*2  volts.  Be2  must,  therefore,  have  been  increased  by 
3'2  volts ;  that  is,  by  one  in  two  hundred.  The  current  c,  there- 
fore, ought  to  have  been  increased  by  one  in  four  hundred,  or  from 
200  to  200'5.  But  in  these  experiments  the  flame  is  never 


CONDUCTIVITY   OF   SALT  VAPOURS 


73 


perfectly  steady,  so  that  the  galvanometer  deflection  always 
oscillates  slightly,  so  that  so  small  an  increase  could  not  have 
been  detected.  In  this  way  it  is  easy  to  explain  the  fact  that 
although  the  salt  vapour  is  a  much  better  conductor  than  the 
flame,  yet  it  has  no  effect  on  the  current,  except  at  the  negative 
electrode.  The  reason  is  that  since  nearly  all  the  fall  of  potential 
takes  place  close  to  the  negative  electrode,  that  is,  that  practically 
all  the  resistance  to  the  passage  of  the  current  is  close  to  this 
electrode,  increasing  the  conductivity  of  the  rest  of  the  flame  is 
practically  without  effect. 

When   salt   is   put   on    the    negative   electrode   the   drop   of 
potential  there  is  greatly  diminished,  so  that  the  distribution  of 


en 

30 

20 

10 

o 

Cu 

rre 

tit 

2  x 

io~)6  A 

up. 

E.M.F 

o-; 

rVc 

Id 

i, 

m^ 

*•*»*. 

12345     cms. 

FIG.  15. 

potential  is  changed  to  a  nearly  uniform  potential  gradient  from 
one  electrode  to  the  other;  that  is,  the  resistance  is  nearly 
uniformly  distributed.  In  this  case,  if  a  part  of  the  flame  is  filled 
with  salt  vapour,  the  total  resistance  is  nearly  proportional  to  the 
length  left  free  from  salt,  so  that  the  current  is  nearly  inversely 
proportional  to  this  length. 

If  the  positive  electrode  is  moved  to  the  end  of  the  flame,  so 
that  it  becomes  much  cooler  than  the  negative  electrode,  the  fall 
of  potential  takes  place  mainly  at  the  positive  electrode,  and  then, 
as  we  should  expect,  the  current  is  increased  when  salt  is  put  on 
the  positive  electrode,  but  not  when  it  is  put  on  the  negative 
electrode. 

Fig.  15  shows  the  distribution  of  potential  with  potassium 
carbonate  on  the  negative  electrode  for  a  total  P.D.  of  07  volt, 


74 


ELECTRICAL  PROPERTIES   OF  FLAMES 


and  Fig.  16  that  with  potassium  carbonate  on  both  electrodes,  but 
not  in  the  space  between  the  electrodes.  These  two  figures  are 
taken  from  a  paper  by  E.  Gold.1 

When  the  flame  is  completely  filled  with  salt  vapour  the 
distribution  of  potential  between  the  electrodes  becomes  again 
similar  to  that  in  a  flame  free  from  salt,  the  current  being, 
however,  much  greater  for  a  given  potential  difference. 

For  experiments  on  flames  filled  with  salt  vapour,  it  is  best 
to  use  a  method  devised  by  Gouy.2  A  salt  solution  is  sprayed  by 
means  of  compressed  air,  and  the  air  and  spray  are  mixed  with 
coal  gas,  so  that  the  mixture  gives  a  Bunsen  flame  uniformly 


10 


FIG.  16. 

filled  with  salt  vapour.  Fig.  17  shows  the  apparatus  used  by  the 
writer  3  in  one  series  of  experiments. 

Carefully  regulated  supplies  of  coal  gas  and  air  were  mixed 
together,  along  with  spray  of  salt  solution,  and  the  mixture  burnt 
from  a  brass  tube  0*7  cm.  in  diameter.  The  air  supplied  by  the 
water  pump  P  partly  escapes  by  bubbling  through  mercury  in  B, 
and  then  passes  into  a  carboy  A.  From  A  the  air  passes  through 
a  flask  W  containing  water,  to  the  sprayer  S,  and  its  pressure  is 
measured  by  the  water  manometer  M.  The  air  supply  is  regulated 
by  means  of  a  pinch-cock  K,  and  by  altering  the  water  supply  to 
the  pump. 

The  coal  gas  was  passed  through  a  regulator  R  into  a  gasometer 
H,  from  which  it  passed  through  a  constriction  L  into  the  globe 

1  Proc.  Roy.  Soc.  A.  vol.  79,  1907. 

2  Ann.  de  Ghimie  et  de  Phys.  [5],  t.  xviii.  p.  25. 

:{  Phil  Trans.  Roy.  Soc.  A.  vol.  192,  pp.  499-528,  1899. 


CONDUCTIVITY   OF   SALT   VAPOURS 


75 


Gr,  where  it  mixed  with  the  air  and  spray.  The  gas  pressure  was 
indicated  by  a  manometer  M'.  The  mixture  passed  into  a  globe 
G',  where  the  coarser  spray  settled,  and  then  to  the  flame  F. 

With  an  apparatus  of  this  kind  a  very  steady  flame  containing  a 
definite  amount  of  salt  vapour  can  be  obtained.  The  amount  of 
salt  in  the  flame  is  proportional  to  the  strength  of  the  solution 
used. 

The  relation  between  the  current  and  potential  difference  has 
been  examined  in  flames  filled  with  alkali  salt  vapours  by 
Arrhenius;1  Smithells,2  Dawson  and  the  writer,  and  by  the 
writer.3 

Arrhenius  measured  the  current  between  two  vertical  parallel 


FIG.  1-7. 

platinum  electrodes.  He  found  that  the  relation  between  the 
current  and  P.I),  could  be  expressed  approximately  in  all  cases  by 
the  equation  C  =  A^/K/(V),  where  A  is  constant,  depending  on 
the  metal,  but  the  same  for  all  salts  of  any  one  metal,  K 
the  concentration  in  gram  molecules  per  litre  of  the  solution 
sprayed,  and  /(V)  denotes  a  function  of  the  P.D.  between  the 
electrodes,  which  has  the  same  values  for  all  salts.  Thus,  with  a 
constant  P.D.,  the  current  was  proportional  to  the  square  root  of  ' 
the  amount  of  salt  in  the  flame. 

Arrhenius'  electrodes  were  0'56  c.m.  apart,  so  that  we  should 

1  Wied.  Ann.  vol.  xlii.  1891.          2  Phil.  Trans.  A.  vol.  193,  p.  89,  1899. 
3  Phil.  Trans.  A.  vol.  192,  p.  499,  1899. 


76 


ELECTRICAL   PROPERTIES    OF   FLAMES 


expect  the  term  Keel  in  the  equation  V  =  Acd  +  Be2  to  be  small 
compared  with  Be2  when  c  is  not  too  small. 

Consequently  for  large  values  of  V  we  should  expect  /(V)  to  be 
proportional  to 


,  so  that  c  =  A^/KV. 
The  following  table  contains  Arrhenius'  results  for  potassium 
iodide,  the  unit  of  current  being  10-8  ampere.     The  currents  are 
the  difference  between  the  current  with   salt  and  that  without 
any. 


Concentration  of  Solution. 

E  M  F.  in 

Clark's  Cell. 

Normal  =  1. 

i 

4 

TV 

eV 

*** 

T0^2T 

nfW 

1 

540 

248 

120 

52-2 

20 

6-9 

2-7 

2 

616 

284 

139 

59-9 

23 

7-9 

2-9 

5 

734 

360 

174 

75-8 

29-1 

10-1 

3'7 

10 

1009 

464          225 

99-7 

37-4 

13-0 

47 

20 

1340 

616          298 

130 

49-6 

17-2 

6-3 

40 

1920 

811 

427 

186 

71-2 

24-8 

9-0 

An  examination  of  these  numbers  shows  that  the  current  varies 
rather  more  rapidly  than  ^/K,  and  that  it  is  nearly  proportional 
to  ^/V  when  V  is  greater  than  that  due  to  two  cells.  Arrhenius 
found  that  the  conductivity  of  the  alkali  salt  vapours  in  the  flame 
increased  rapidly  with  the  atomic  weight  of  the  metal. 

The  fact  that  all  salts  of  any  one  metal  gave  equal  currents  was 
explained  by  Arrhenius  by  supposing  that  they  were  all  converted 
into  hydroxides  by  the  water  vapour  present  in  the  flame. 

Arrhenius'  results  were  confirmed  and  extended  by  Smithells, 
Dawson,  and  the  writer  (loc.  cit.).  The  current  was  measured 
between  two  concentric  cylinders  with  their  axis  vertical  in  a 
Bunsen  flame  containing  salt  vapour. 

The  inside  cylinder  was  hotter  than  the  outside  one,  and  a 
current  was  always  obtained  when  the  electrodes  were  connected 
to  the  galvanometer  without  any  battery  in  the  circuit. 

Fig.  18  shows  the  relation  between  the  current,  from  the  inside 
to  the  outside  cylinder,  and  P.D.  when  a  ^  normal  solution  of 
potassium  nitrate  was  sprayed. 

It  will  be  seen  that  the  current  is  much  greater  when  the 


CONDUCTIVITY   OF   SALT   VAPOURS 


77 


outside  cylinder  is  negative  than  when  it  is  positive.  Since  V  =  Ei2 
approximately,  where  i  is  the  current  density  at  the  negative 
electrode,  we  get  V  =  Bc12/(2^r1/)2  and  V  =  Bc2z/(2nrJ)z,  where  I  is 
the  length  of  the  cylinders,  i\  the  radius  of  the  outside  one,  r.2  that 
of  the  inside  one,  and  cx  the  current  with  the  outside  cylinder 
negative,  and  c9  that  with  the  inside  cylinder  negative.  Hence 
e1/c2  =  rjrz.  For  the  cylinders  used,  rjr2  was  about  2,  whereas  in 
the  above  diagram  c-1/c2  for  5  volts  is  about  3,  but  the  calculation 
assumes  the  two  cylinders  to  be  at  the  same  temperature. 


150 


-3      -* 


SO 

FIG.  18. 

When  the  P.D.  was  zero,  there  was  a  current  from  the  inside 
cylinder  to  the  outside  one.  This  shows,  of  course,  that  the 
equation  V  =  Adc  -f-  Be2  cannot  be  true  in  this  case,  when  V  is 
very  small.  The  explanation  of  this  current  is  probably  as  follows. 
The  negative  ions  in  the  flame  have  a  much  higher  velocity  than 
the  positive  ions,  so  that  they  diffuse  more  quickly.  Consequently, 
an  insulated  electrode  immersed  in  the  flame  acquires  a  small 
negative  potential  sufficient  to  make  the  rate  at  which  negative 
ions  fall  on  it  equal  to  the  rate  at  which  positive  ions  fall  on  it. 
This  potential  is  greater  the  higher  the  temperature.  Con- 
sequently the  outside  cylinder  tends  to  take  up  a  higher  potential 


78 


ELECTRICAL  PROPERTIES   OF   FLAMES 


than  the  inside  one.  The  hot  electrodes  in  the  flame  emit  ions, 
and  this  emission  is  probably  increased  by  the  salt  vapour.  If  an 
electrode  is  emitting  negative  ions  it  will  tend  to  acquire  a  positive 
charge,  so  that  there  may  be  an  effect  due  to  this  cause  in  the 
opposite  direction  to  that  due  to  diffusion.  These  effects,  how- 
ever, are  small,  and  can  usually  be  neglected  when  the  potential 
difference  between  the  electrodes  is  above  two  or  three  volts. 

The  relation  between  the  current  and  P.D.  for  small  P.D.'s  is 

Upper  Electrode  Positive 
o  5  $  S 


Lorfer   Electrode  Negative. 
FIG.   19. 

complicated  by  such  effects  as   those  just  mentioned,  which  are 
difficult  to  allow  for  accurately. 

The  distribution  of  potential  between  the  electrodes  L  in  a 
flame  containing  rubidium  chloride  is  shown  in  Fig.  19.  The 
electrodes  were  horizontal  wire  gratings. 

It  will  be  seen  that  the  uniform  gradient  is  very  small,  although 
the  current  with  120  volts  was  about  2  x  10  ~4  ampere.  The 
lower  electrode  consisted  of  a  gauze  with  wires  3  mms.  apart, 
while  the  upper  one  had  wires  about  1  mm.  apart.  The  upper 
electrode  was  cooler  than  the  lower  one. 

1  H.  A.  Wilson,  Phil.  Trans.  A.  vol.  192,  p.  507,  1899. 


CONDUCTIVITY   OF   SALT   VAPOURS 


79 


cms. 


Fig.  20  shows  the  change  in  the  distribution  of  potential  when 
the  upper  electrode  is  changed  from  positive  to  negative.  With 
the  lower  one  positive,  there  is  no  drop  near  to  it.  The  lower 
electrode,  which  was  very  hot  in  these  experiments,  therefore 
must  have  emitted  a  thermionic  positive  current,  for  otherwise 
there  ought  to  have  been  a  small  drop  at  it. 

In  these  experiments  the  upward  current  of  the  flame  gases 
carries  a  continuous  supply  of  ions  up 
through  the  lower  electrode.  Con- 
sequently, if  the  lower  electrode  is 
positively  charged  it  will  attract  the 
negative  ions  from  the  gas  as  they  pass 
through  it,  so  that  the  gas  will  acquire 
a  positive  charge.  The  theory  of  the 
variation  of  the  potential  near  the  elec- 
trodes is  complicated  by  this  supply  of 
ions  from  below. 

Marx  l  made  estimates  of  the  order 
of  magnitude  of  the  ionic  velocities 
in  flames  containing  salt  vapours,  by  applying  the  theory  of  the 
variation  of  the  potential  near,  plane  electrodes  in  a  gas  at 
rest  to  his  observations  with  horizontal  coarse  grating  electrodes 
in  the  flame.  He  made  use  of  J.  J.  Thomson's  layer  theory, 
described  in  a  previous  chapter.  The  results  are  of  little  value, 
owing  to  the  theory  used  not  applying  when  the  ionized  gas  is 
streaming  through  grating  electrodes.  Moreover,  the  method  is 
of  little  use,  even  in  cases  to  which  the  theory  does  apply. 
Marx's  lower  grating  had  wires  3  mms.  apart,  and  he  used  measure- 
ments of  the  potential  taken  up  by  a  wire  parallel  to  the  grating, 
made  at  distances  from  the  grating  as  small  as  O35  mm.  At 
such  distances  from  the  grating  the  lines  of  flow  of  the  current 
must  have  been  nearly  normal  to  the  surface  of  the  grating  wires, 
and  so  not  perpendicular  to  the  exploring  wire.  Also  the  effective 
area  of  the  electrodes  must  have  been  more  nearly  equal  to  the 
area  of  the  surface  of  the  wires  than  to  the  area  of  the  grating. 
In  view  of  these  considerations,  I  do  not  think  Marx's  experiments 


Ann.  d.  Phys.  vol.  iv.  p.  2,  1900. 


80 


ELECTRICAL  PROPERTIES   OF  FLAMES 


can  be  regarded  as  giving  even  the  order  of  magnitude  of  the 
ionic  velocities. 

All  that  can  be  deduced  from  the  distribution  of  potential 
between  the  horizontal  grating  electrodes  is  that  when  both  are 
equally  hot  the  velocity  of  the  negative  ions  is  probably  con- 
siderably larger  than  that  of  the  positive  ions,  for  the  variation  of 
the  potential  near  the  negative  electrode  is  more  rapid  than  near 
the  positive  electrode. 

THE  VELOCITY  OF  THE  IONS  OF  SALT  VAPOURS  IN  FLAMES 

The  velocity  of  the  positive  ions  of  alkali  salt  vapours  in  flames 
was  estimated  by  the  writer1  by  finding  the  potential  gradient 
required  to  make  them  move  down  the  flame  against  the  upward 
stream  of  gases.  The  apparatus  used  is  shown  in  Fig.  21. 


FIG.  21. 


F  Flame  inside  glass  cylinder,  resting  on  wooden  block  W.  and  covered  with 

metal  plate  T. 

EE  Grating  electrodes. 

PP  Screen  above  lower  electrode. 

AA  Bead  of  salt  and  support. 

CC'  Commutators. 

B  Battery. 

G  Galvanometer. 

1  Phil.  Trans.  A.  vol.  192,  p.  499,  1899. 


CONDUCTIVITY   OF  SALT  VAPOURS 


81 


A  bead  of  salt  was  put  in  the  flame  just  below  the  upper 
electrode,  and  the  current  from  the  lower  electrode  measured.  It 
was  found  that  when  the  upper  electrode  was  positive,  introducing 
the  bead  caused  no  increase  in  the  current  unless  the  potential 
difference  between  the  electrode  was  greater  than  100  volts,  when 
the  electrodes  were  5  cms.  apart.  When  the  upper  electrode 
was  negative,  other  conditions  being  the  same,  the  current  was 
increased  on  introducing  the  bead,  even  with  one  or  two  volts. 

To  prevent  any  ions  reaching  the  lower  electrode  by  passing 
down  the  sides  of  the  flame,  where  the  velocity  of  the  gases  is 


small,  a  screen  was  placed  above  the  lower  electrode.  This  was  of 
platinum  gauze,  with  a  hole  in  the  middle  2  cms.  in  diameter. 
This  hole  was  filled  up  by  the  flame,  which  also  passed  through 
the  gauze  around  the  hole.  The  lower  electrode  was  bent  up  so 
that  it  was  only  2  or  3  mms.  below  the  screen.  The  screen  was 
connected  to  the  battery,  so  that  the  galvanometer  only  received 
the  current  going  through  the  hole  in  it  to  the  lower  electrode. 

Fig.  22  shows  the  results  obtained  with  a  bead  of  potassium 
carbonate.  It  will  be  seen  that  the  bead  did  not  appreciably 
increase  the  current  when  the  upper  electrode  was  positive,  unless 
the  P.D.  was  above  about  100  volts.  The  P.D.  required  to  increase 
the  current  with  the  upper  electrode  positive  was  found  to  be 
about  100  volts  for  all  salts  of  caesium,  rubidium,  potassium, 
sodium,  and  lithium.  The  possible  error  in  the  necessary  P.D. 
was  rather  large,  especially  in  the  case  of  sodium  and  lithium, 


82          ELECTRICAL   PROPERTIES    OF   FLAMES 

which  only  gave  a  small  increase,  even  with  large  potentials.  The 
value  100  volts  was  probably  correct  within  20  per  cent.  The 
potential  gradient  in  the  upper  part  of  the  space  between  the 
electrodes  was  found  to  be  3'3  volts  per  cm.  without  any  salt,  when 
the  P.D.  was  100  volts.  The  introduction  of  the  salt  lowers  the 
potential  gradient  in  the  part  of  the  flame  filled  with  salt  vapour 
to  practically  zero,  so  that  it  increases  the  fall  of  potential  in  the 
rest  of  the  flame. 

In  the  present  case,  if  the  salt  vapour  occupied  2  cms.  of 
the  flame  it  would  increase  the  fall  of  potential  at  the  negative 
electrode  by  6'6  volts.  The  drop  at  the  negative  electrode  was 
84  volts,  so  that  since  the  current  is  proportional  to  the  square 
root  of  the  drop,  the  current  ought  to  have  been  increased  by  3'3 
in  84,  or  4  per  cent.  The  current  was  eight  scale  divisions,  so  that 
this  increase  could  not  be  detected.  Since  the  uniform  gradient 
in  the  absence  of  salt  is  proportional  to  the  current,  it  must  have 
been  increased  by  4  per  cent,  to  3*31  volts  per  cm.  Obviously,  the 
gradient  which  is  required  is  that  just  below  the  salt  vapour,  and 
not  that  in  it,  which  is  very  small. 

The  average  velocity  of  the  gases  in  the  burner  tube  was  found 
to  be  206  cms.  per  second  from  the  volume  passing  through.  The 
diameter  of  the  flame  was  about  2*5  cms.,  which  indicates  a  cross- 
section  about  thirteen  times  that  of  the  tube.  Owing  to  the 
rise  of  temperature,  an  expansion  of  about  eight  times  might  be 
expected,  but  gas  enters  the  flame  along  its  sides.  Since  the 
pressure  of  the  gas  in  the  tube  is  very  nearly  equal  to  atmospheric 
pressure,  it  seems  clear  that  the  velocity  in  the  flame  must  be 
practically  the  same  as  that  in  the  tube,  in  spite  of  the  change  of 
volume,  because  there  is  no  pressure  difference  available  to 
change  the  velocity.  Hence  we  get  for  the  apparent  velocity 
of  the  positive  ions  of  any  alkali  salt  due  to  one  volt  per  cm. 
206  cms. 

3-3   :       2  sec. 

It  has  been  assumed  so  far  that  if  the  positive  ions  move 
down  the  flame  they  will  increase  the  current,  and  the  fact  that 
an  increase  is  observed  above  a  definite  P.D.  was  supposed  to 
justify  this  assumption.  The  precise  way  in  which  the  current 
is  increased  remains  to  be  considered. 


CONDUCTIVITY   OF   SALT   VAPOURS  83 

In   the  uniform  gradient   the   current,  as  we    have  seen,1  is 
independent  of  the  velocity  of  the  gases,  and  given  by 
i  =  Xe9t(£j  -f-  ^2)- 

When  the  salt   is  put  in    the   uniform  gradient  in  the    salt 
vapour  is  given  by 


where  X'  is  very  small  compared  with  X  and  n  large  compared 
with  n  ;  k^  and  kz'  are  probably  of  the  same  order  as  7^  and  k.2. 
Hence,  at  the  critical  P.D.  — 

Xrc^  +  k2)  =  XV(/,V  +  V)- 

At  the  edge  of  the  salt  vapour  X  changes  to  X',  so  that  there 
will  be  a  layer  of  charge  in  the  gas  there.  The  positive  ions  of 
the  salt  do  not  move  down  at  the  critical  P.D.,  so  that  below  the 
salt  X  must  be  practically  unaltered,  as  we  have  seen. 

If  now  the  P.D.  is  slightly  increased,  the  positive  salt  ions 
move  down  slowly.  As  they  go  down  they  will  continually  re- 
combine  with  the  negative  flame  ions  present,  and  continually  be 
reionized.  Thus  the  conductivity  of  the  flame  below  the  salt 
will  now  be  increased,  and  when  the  salt  ions  get  to  the  negative 
electrode  they  will  accumulate  there  and  diminish  the  fall  of 
potential.  The  increase  of  the  current,  it  will  be  observed,  is 
almost  entirely  due  to  the  effect  of  the  positive  ions  on  the  drop 
of  potential  at  the  negative  electrode,  and  not  to  the  increase  in 
the  conductivity  in  the  uniform  gradient. 

The  maximum  possible  increase  of  the  conductivity  in  the 
uniform  gradient  below  the  salt  vapour  can  be  easily  calculated. 
Suppose  the  current  without  salt  is  i0,  and  with  salt  i,  and  let  X0 
be  the  minimum  gradient  required  to  make  the  positive  ions 
move  down.  Then,  below  the  salt  the  gradient  cannot  be  less 
than  X0,  so  that  the  conductivity  below  the  salt  cannot  be  increased 
more  than  in  the  ratio  i/i0,  for  X0  is  the  gradient  when  the  ions 
just  do  not  move  down,  and  therefore  is  equal  to  the  gradient  in 
the  free  flarne  corresponding  to  i0.  Consequently,  just  above  the 
critical  P.D.,  the  concentration  of  the  salt  ions  moving  down  must 
be  extremely  small,  but  they  accumulate  at  the  negative  electrode, 
and  so  produce  an  appreciable  effect  there. 

1  See  p.  63. 


G  2 


84         ELECTRICAL   PROPERTIES    OF   FLAMES 

It  appears,  therefore,  that  the  salt  ions  which  move  down  are 
not  charged  ions  all  the  time,  but  must  be  continually  recombining 
and  reionizing.  Since  they  produce  an  effect  when  they  get  to 
the  lower  electrode,  it  is  clear  that  they  must  differ  from  the 
flame  ions,  so  they  cannot  be  hydrogen  ions.  It  is  natural  to 
suppose  that  they  are  atoms  of  the  alkali  metal  as  in  salt  solutions. 
Suppose  that  a  particular  metal  atom  is  ionized  for  a  fraction  / 
of  the  time,  then  if  it  just  moves  down  the  flame  this  means  that 
/(^X  —  u)  =  (1  —f)u  or  /A^X  =  «,  where  u  is  the  velocity  of  the 
flame  gases,  for  while  the  atom  is  not  charged  it  will  be  carried 
upwards  with  velocity  u.  It  appears,  therefore,  that  the  quantity 
determined  in  the  experiment  described  is  fk^  and  not  kr  It  is 
convenient  to  call/A^  the  apparent  velocity  of  the  positive  salt  ions. 

This  experiment  has  been  repeated  by  Mr.  Lusby.1  He  found 
that  the  critical  P.D.  was  62  volts  for  all  salts  of  alkali  and 
akaline  earth  metals.  The  distance  between  his  electrodes  was 
only  3  cms.,  which,  unfortunately,  was  not  enough  to  allow  the 
uniform  gradient  to  be  well  developed  in  the  absence  of  salt,  for 
the  space  occupied  by  the  negative  drop  was  over  2  cms.  With 
the  salt  in,  he  observed  a  very  small  gradient  for  nearly  2  cms. 
below  the  upper  electrode,  which  was  evidently  due  to  this  part 
of  the  flame  containing  salt  vapour.  He  found  the  uniform 
gradient  without  salt  to  be  6*5  volts  per  cm.,  and  the  velocity  of 
the  flame  to  be  206  cms.  per  sec.  This  gives 


"l4/  "     6'5         "sec. 
which   agrees  as  well  as  could   be   expected  with   the  value  of 

62 '  I  found,  for  his  uniform  gradient  was  too  short  (0'2  cm.) 

sec. 

to  be  measured  at  all  exactly.  He  used  the  value  of  the  gradient 
found  with  salt  vapour2  to  calculate  ^/,  but  this  is  obviously 
incorrect.  What  is  required  is  the  gradient  just  below  the  salt 
vapour,  which,  since  the  current  is  the  same,  should  be  the  same 
as  without  salt. 

Moreau  3  estimated  the  apparent  velocity  of  the  positive  ions 

1  Proc.  Camb.  Phil  Soc.  vol.  xvi.  part  i.  1910. 

2  Lusby  got  k,  f  =  300  cms>  by  using  the  gradient  found  with  salt  in.     A 

sec. 
very  minute  trace  of  salt  vapour  is  enough  to  greatly  diminish  the  gradient. 

3  Journal  de  Physique  (4),  vol.  ii.  p.  558. 


CONDUCTIVITY   OF   SALT  VAPOURS  85 

of  sodium  and  potassium  salts  by  finding  the  potential  gradient 
required  to  make  them  move  across  the  flame  from  the  bottom  of 
one  vertical  electrode  to  the  top  of  another.  In  this  way  he  found 
fcj/  =  80  cms.  per  sec.,  which  agrees  well  with  62  cms.  per  sec. 

Marx's  estimate  of  the  order  of  magnitude  of  7jlt/has  already 
been  discussed.  He  found  k^f  to  be  about  250  cms.  per  sec.,  which 
is  of  the  same  order  as  60. 

OTY1S 

The  mean  of  32,  62,  and  80  is  58 ',  which  may  be  taken  to 

sec. 

be  the  most  probable  value  of  Tc^f  and  is  probably  correct  within 
50  per  cent. ;  Js^f,  of  course,  must  vary  in  different  flames,  and  in 
different  parts  of  the  same  flame. 

If  the  positive  ions  consist  of  atoms  of  the  metal,  we  should 
expect  fcj  to  be  nearly  inversely  proportional  to  the  square  root 
of  the  atomic  weight  of  the  metal. 

Now,  the  conductivity  due  to  a  definite  amount  of  salt  increases 
rapidly  with  the  atomic  weight,  so  that  /  must  be  much  smaller 
for  lithium  than  for  caesium.  If  we  suppose  that  when  the 
concentration  of  the  salt  vapour  is  very  small  /  is  proportional  to 
the  square  root  of  the  atomic  weight  of  the  metal,  and  &x  inversely 
proportional,  then  the  product  &lt/  would  be  constant,  as  is  found 
to  be  the  case. 

It  is  probable  l  that  for  caesium  /  is  nearly  unity, 2  so  that, 
assuming  this,  we  get  the  following  values  of  ^ : — 


Atomic  Weight. 

1* 

Caesium  .         .   ..   "..'        .       •_» 
Rubidium       "••"'•_     • 
Potassium     -  .        .   "     .     .  . 
Sodium    .       .-«..'••        .- 
Lithium  .         .         .        .      '  .  • 

133 

85-4 
39-2 
23-1 
7-0 

58 
72 
107 
139 

i         253 

I  think  it  is  more  probable  that  these  numbers  are  too  large 
than  too  small.  The  value  of  k:  to  be  expected  on  the  kinetic  theory 
can  only  be  estimated  very  roughly,  because  the  necessary  data  as 
to  the  free  path  of  the  ion,  etc.,  have  to  be  guessed  at,  in  the  flame. 

1  H.  A.  Wilson,  Phil.  Mag.,  June  1911. 

2  If  /  for  caesium  is  less  than  unity  then  the  values  of  fcj  will  be  corre- 
spondingly greater.    (See  page  110.) 


86         ELECTRICAL   PROPERTIES   OF   FLAMES 

The  temperature  of  a  Bunsen  flame  is  above  the  melting-point 
of  platinum,  because  very  thin  wires  will  melt  in  it,  so  that  it 
cannot  be  much  below  2000°  C.  Estimates  made  by  putting  in 
thermocouples  are,  of  course,  too  low,  because  the  couple  radiates, 
and  so  does  not  take  up  the  true  temperature.  According  to  the 

kinetic  theory,  we  have  Jc,  =  2A/,rr        ?,  where  e  is  the  charge  on 

\  27i  mV 


the  ion,  A  its  mean  free  path,  w  its  mass,  and  V  the  square  root 
of  the  mean  square  of  its  velocity  of  agitation. 

The  flame  contains  N2,  H2O,  CO,  H2,  etc.  Of  these  N2  is 
present  in  the  largest  quantity.  The  free  path  of  a  nitrogen 
molecule  in  nitrogen  at  0°  and  760  mms.  is  9'5  X  10  ~6  cm.1  At 
2000°  C.  this  gives  7'9  X  10~5  cm.  The  free  path  of  an  atom  of 
caesium  is  probably  smaller  than  that  of  a  molecule  of  nitrogen, 
so  that  I  shall  take  the  free  path  of  a  caesium  atom  in  the  flame 
to  be  4  x  10  ~5  cm.  The  velocity  of  agitation  of  a  hydrogen 
molecule  at  0°  C.  is  1'84  x  105  cms.  per  sec.,  so  that  for  a  caesium 
atom  at  2000°  C.  we  get 


V  =  1-84  x  W  X  ,  =  6-5  x  10.. 


Also  e/m  for  a  caesium  atom  carrying  the  same  charge  as  a 
hydrogen  atom  in  solutions  is  equal  to  7  2  '5  in  electromagnetic  units. 

.    el         1-4  x  72-5  x  4  x  10~5  x  108 
Hence,   we   get   k,  =       1          =  _6___ 


=  6'3        -  for  one  volt  per  cm.     This  is  nearly  ten  times  smaller 
sec. 

than  the  value  58  found  for  caesium  on  the  assumption  that  /  is 
unity  for  this  metal,  but  the  data  used  in  the  calculation  of  kv 
and  also  the  formula  employed  are  so  doubtful  that  no  weight  can 
be  attached  to  the  discrepancy.  The  experimental  result  and  the 
theoretical  value  are  of  the  same  order  of  magnitude,  which  is  all 
that  could  be  expected. 

I  think,  therefore,  that  there  is  no  reason  to  doubt  that  the 
positive  ions  of  alkali  salt  vapours  in  flames  are  atoms  of  the 
metal,  as  in  solutions.  This  view  is  powerfully  supported  by 
the  fact  discovered  by  Lenard  that  the  yellow  coloration  of  the 

1  Meyer's  Kinetic  Theory  of  Gases,  p.  192. 


CONDUCTIVITY   OF   SALT   VAPOURS  87 

flame  by  sodium  salts  is  attracted  by  a  negatively  charged 
electrode  in  the  flame. 

If  two  platinum  wires  are  put  in  a  Bunsen  flame,  one  above 
the  other,  and  some  sodium  carbonate  is  put  on  the  upper  one, 
then  if  the  wires  are  connected  to  a  battery  giving  a  few  hundred 
volts,  or  to  an  induction  coil,  sodium  light  appears  at  the  lower 
wire  when  it  is  the  negative  pole,  but  not  when  it  is  positive.1 
This  clearly  shows  that  the  positive  ions  contain  the  metal,  and 
effectually  disposes  of  the  suggestion  that  the  positive  ions  of  salt 
vapours  in  flames  consist  of  hydrogen  atoms.  If  they  were 
hydrogen  atoms  it  would  be  difficult  to  explain  the  increase  in 
the  current  above  the  critical  P.D.,  for  hydrogen  atoms  going 
down  would  not  increase  the  conductivity  at  the  negative  electrode. 
Moreover,  salt  vapours  enormously  increase  the  conductivity  of 
the  cyanogen  flame,  which  contains  no  hydrogen.2 

The  velocities  of  the  ions  of  salt  vapours  in  air  at  about 
1000°  C.  was  estimated  by  the  writer,3  using  a  method  similar  to 
that  used  in  the  flame.  A  mixture  of  air  and  spray  of  salt  solution 
was  passed  through  a  platinum  tube  heated  to  a  bright  red  heat 
in  a  gas  furnace.  The  P.D.  required  to  make  the  ions  of  the  salt 
vapour  move  against  the  stream  of  hot  air  on  emerging  from  the 
tube  was  found  in  the  same  way  as  in  the  flame. 

In  this  case  there  was  practically  no  current  until  the  critical 
P.D.  was  reached,  so  that  the  potential  gradient  could  be  taken  to 
be  uniform  without  serious  error.  The  critical  P.D.  was  found  to 
be  25  volts  for  the  positive  ions  of  all  the  alkali  salts,  and  48  volts 
for  salts  of  Ca,  Sr,  and  Ba.  For  the  negative  ions  of  all  salts  of 
alkali  metals  and  alkaline  earth  metals  the  critical  P.D.  was  7  volts. 

The  velocity  of  the  air  current  was  160  cms.  per  sec.,  so  that 
the  apparent  ionic  velocities  were — 

(1)  Negative  ions     .     ...     .."..*.     .     .      26 


(2)  Positive  ions  of  alkali  metals 7*2 


sec 

cms. 

sec. 

(3)  Positive  ions  of  alkaline  earth  metals    .     .     3*8 

sec. 

1  H.  A.  Wilson,  KL  Lecture,  February  12,  1909. 
a  Smithells,  Dawson  and  Wilson  (loc.  cit.). 
3  Loc.  cit. 


88         ELECTRICAL  PROPERTIES   OF   FLAMES 

The  possible  error  in  these  experiments  was  large,  and  the 
values  obtained  can  only  be  regarded  as  giving  the  order  of 
magnitude  of  the  velocities. 

The  free  path  of  an  air  molecule  in  air  at  0°  C.  and  760  mms. 
is  9'6  x  10-6  cms.  At  1000°  C.  this  becomes  4*5  x  10~5  cms.  For 
a  caesium  atom  carrying  the  same  charge  as  a  monovalent  ion  in 
solutions  e/m  =  72'5,  and 

VI  97^  v  9 
=  4'9  x  104- 

If  we  assume  that  the  free  path  of  the  caesium  atom  is  one- 
half  that  of  an  air  molecule,  we  get 

,        1-4  x  72-5  x  2-3  x  1Q-5  x  108 
*>  =  4-9  x  10*  t-8  cms>  Per  sec- 

for  one  volt  per  cm.  This  agrees  as  well  as  could  be  expected 
with  the  value  7*2  found  if  we  assume  that  for  caesium  /  is  about 
unity.  For  the  lighter  metals  we  may  suppose  that  /  is  smaller 
than  unity,  as  in  flames. 

The  distribution  of  the  electric  force  in  flames  shows  that  the 
velocity  of  the  negative  ions  must  be  much  larger  than  that  of 
the  positive  ions.  The  writer  and  others 1  attempted  to  find  the 
velocity  of  the  negative  ions  by  the  same  method  as  was  used  for 
the  positive  ions,  and  results  varying  from  1000  to  more  than 
10,000  were  obtained.  When  the  upper  electrode  is  negatively 
charged,  putting  in  the  salt  increases  the  current,  even  with 
small  potential  differences.  Fig.  23  shows  the  results  obtained 
by  the  writer.2 

It  will  be  observed  that  the  current  with  salt  increases  rapidly 
at  about  one  volt,  and  it  was  supposed,  therefore,  that  this  was 
the  critical  P.D.  The  current,  however,  is  very  considerably 
increased  by  the  salt,  even  with  zero  P.D. 

When  the  upper  electrode  is  negatively  charged  there  is  a 
large  potential  drop  at  it,  and  a  uniform  gradient  between  the 
electrodes,  which  is  proportional  to  the  current  and  independent 
of  the  velocity  of  the  gas.  When  salt  is  put  in  near  the  upper 
•electrode  the  large  drop  there  is  diminished,  and  so  the  uni- 
form gradient  and  the  current  must  be  increased,  whether  the 

1  Moreau  and  E.  Gold.  2  Phil  Trans.  A.  vol.  192,  1899. 


CONDUCTIVITY   OF  SALT   VAPOURS 


89 


negative  ions  move  down  the  flame  or  not.  Thus  the  method 
used  for  the  positive  ions  is  not  applicable  to  the  negative  ions, 
and  the  supposed  determinations  of  the  velocity  of  the  negative 
ions  made  by  it  are  of  no  value.  Indirect  determinations,  which 
will  be  discussed  in  later  chapters,  show  that  the  velocity  of  the  I 
negative  ions  is  about  10,000  cms.  per  sec.  for  1  volt  per  cm. 
This  is  about  what  we  should  expect  if  the  negative  ions  were 
free  electrons. 

The  free  path  of  an  electron  in  nitrogen  at  2000°  C.  may  be 


FIG.  23. 

taken  to  be  about  31*6  X  10 ~5  cm.;  that  is,  four  times  the  free 
path  of  a  nitrogen  molecule.     The  velocity  of  agitation  is 

V  =  1-84  x  105  x     /2273  x  2  x  1-8  x  JO3  =  3.2  x  1Q7 

V  273 

Taking  e/m  =  1'75  x  107,  we  get 

_  1-4  x  175  x  107  x  31-6  x  10~5  x  lO8 

3-2  x  107 

=  24,400  cms.  per  sec.  for  1  volt  per  cm. 

Probably  the  actual  free  path  is  shorter  than  31*6  X  10  ~5  cm.,  on 
account  of  the  attraction  between  the  electron  and  the  molecules 

If  we  take  &2  =  A  -^  instead  of  1-4  — TT  we  get  Jc9  =  8700. 
-  raV  mV 

If  the  positive  ions  of  alkali  salts  in  flames  consist  of  metal 


90         ELECTRICAL  PROPERTIES   OF  FLAMES 

atoms,  and  the  negative  ions  of  free  electrons,  as  seems  probable, 
then  the  ionization  most  likely  consists  in  the  expulsion  of  an 
electron  from  an  uncharged  atom  of  the  metal.  Or  a  molecule  of 
the  hydrate,  like  KOH,  may  combine  with  an  atom  of  hydrogen, 
forming  water  and  K,  which  at  the  moment  of  its  liberation  emits 
an  electron.  The  precise  way  in  which  the  ions  are  formed  can 
only  be  guessed  at. 

e"k 

Note. — The    theoretical  formula  k  =  ^  — =-T-  was  first  obtained 

mv 

by  Sir  J.  J.  Thomson.  Langevin,  by  allowing  for  the  variation  of 
2,  got  k  =  cA/wiV.  The  writer,1  allowing  also  for  the  variation  of 
V,  got  !'4<?A/mV.  The  value  of  "k  is  probably  diminished  by  the 
action  of  the  charge  on  the  surrounding  molecules.2  In  the  case 
of  heavy  ions  the  velocity  is  probably  really  greater  than  jl/tnV 
on  account  of  the  persistence  of  the  velocities  after  collisions.3 
Sir  J.  J.  Thomson4  has  given  a  theory  according  to  which  the 
velocity  of  a  heavy  ion  is  nearly  independent  of  its  mass  and 
charge,  and  depends  practically  only  on  the  surrounding  gas. 
Calculations  of  k  by  means  of  the  formula  k  =  eA/mV  are  therefore 
of  little  value,  and  cannot  be  relied  on  to  give  more  than  the 
order  of  magnitude  to  be  expected. 

RELATIVE  CONDUCTIVITIES  OF  DIFFERENT  ALKALI  SALTS  IN 

FLAMES 

The  conductivities  imparted  to  a  Bunsen  flame  by  salts  of  the 
alkali  and  other  metals  were  examined  by  Arrhenius  (loc.  cit.). 
He  found  that  the  conductivity  was  the  same  for  all  salts  of  any 
one  metal,  and  was  nearly  proportional  to  the  square  root  of  the 
concentration  of  the  salt  solution  sprayed.  The  conductivity 
increased  rapidly  with  the  atomic  weight  of  the  metal. 

Smithells,  Dawson  and  the  writer  (loc.  cit.)  confirmed  Arrhenius' 
results,  but  found  that  when  the  concentration  of  the  salt  vapours 
was  greater  than  the  concentrations  used  by  Arrhenius,  that  then 
all  salts  of  the  same  metal  did  not  give  equal  conductivities,  and 

1  Phil.  Mag.,  November  1910. 

2  Langevin,  Theses,  Paris,  1902.     Wellisch,  Phil.  Trans.  A.  vol.  109,  1909. 

3  Jeans,  .Kinetic  Theory  of  Gases. 

4  Proc.  Camb.  Phil.  Soc.  vol.  xv.  part  iv.  1909. 


CONDUCTIVITY   OF   SALT  VAPOURS 


91 


that  then  the  conductivity  was  not  always  nearly  proportional  to 
the  square  root  of  the  concentration. 
io~7Amperes. 


£60 

£70 


260 
£50 


£40 


Z30 

azo 


2.10 
200 


190 


/70^ 

160 


150 


100 
90 
00 
70 
60 


50  h 


7 


7 


MO. 


KOH 


Kl 


KBr 

xa 


O-oi  o-oi  o-05  o-i  0-15  02  Normal 

Variation  of  current  with  concentration  of  solution.     E.M.F.,  5-60  volts. 

FIG.  24. 

Fig.  24  shows  the  variation  of  the  current  due  to  5*60  volts 
between  concentric  cylindrical  electrodes,  with  the  concentration 
(C)  of  the  solution  sprayed. 


92 


ELECTRICAL  PROPERTIES   OF   FLAMES 


It  will  be  seen  that  for  concentrations  up  to  about  ¥V  normal 
(a  normal  solution  contains  one  gram  molecule  per  litre)  all  the 
salts  of  potassium  gave  equal  currents.  Above  this  concentration, 
the  current  due  to  oxysalts  increased  more  rapidly  than  that  due 
to  halogen  salts.  For  small  concentrations  the  current  is  nearly 
proportional  to  the  ^/C  in  all  cases.  In  the  case  of  potassium 
chloride  and  potassium  bromide  the  current  is  proportional  to 
^/C  up  to  the  largest  concentrations  tried,  but  for  the  oxysalts 
this  does  not  hold. 

The  following  tables  contain  the  currents  observed  with  three 
potential  differences  for  a  large  number  of  solutions.  These  cur- 
rents are  the  means  of  the  currents  in  opposite  directions.  The 
current  through  the  flame  without  salt  was  subtracted  in  each 
case  from  the  current  observed  when  the  solution  was  sprayed. 
The  unit  of  current  is  10  ~7  amperes. 


Concentration 
of  solution. 

E.M.F. 

KCl. 

31-9 
18-9 
7-34 

KBr. 

KC1O3.        KI. 

KNO3. 

fM* 

|Wo, 

KOH. 

•2  normal 

5-60 
•795 
•227 

31'4 
20-1 
7-32 

30-5 

16-8 
6-62 

86'5 
43-2 
12-8 

193 

70-8 
21-6 

... 

276 
826 
26-6 

•1 

5-60 
•795 
•227 

21-0 
12-4 
5-75 

21-4 
12-4 

5-74 

... 

37-8 
21-3 
6'2 

68-3 
29'3 
9-35 

83-3 
33-4 

11-0 

76-4 
35-4 
11-2 

•05 

5-60 
•795 
•227 

14-1 
9-23 

4-0 

14-7 
10-3 
4-13 

12-9 
8-35 
3-81 

22-8 
12-8 
4-6 

24-5 
13-2 
5-1 

27-5 
13-8 
5-71 

27-6 
14-2 
5-43 

24-1 
12-8 
5'4 

•02 

5-60 
•795 

•227 

8-93 
6-09 
2-97 

... 

:::  '  ::: 

10-2 
6-63 
3-15 

•01 

5-60 
•795 
•227 

6-02 

4-27 
2-17 

6-97 
4-90 
2-23 

6-77 

4-69 
2-32 

6-99 
4-78 
1-97 

7-06 
4-84 
2-47 

6-33 

4-56 
2-30 

6-00 
4'30 
2-20 

6-1 
4-05 
1-86 

•005 

5-60 

5-47 

... 

5-27 

•002 

5-60 
•795 
•227 

... 

4-03 
2-80 
1-50 

3-89 
2-73 
1-24 

... 

3'73 

2-59 
1-45 

CONDUCTIVITY   OF   SALT  VAPOURS 


93 


'oncentration 
of  solution. 

E.M.F. 

NaF. 

Nad. 

XaBr. 

Nal. 

NaNO3. 

fNagSOj. 

yNaaCOa. 

NaOH. 

"5  normal 

5-60 

8-98 

7'66 

9'24 

12-5 

12-6 

11-4 

12-0 

•795 

4-78 

5-37 

5-38 

5-83 

6-64 

6'60 

6-20 

•227 

2-00 

2-07 

2-11 

2-21 

... 

2-49 

2-45 

2-61 

•2 

5-60 

4-03 

4-54 

5-56 

6-72 

5-73 

5-99 

5-67 

•795 

2-65 

3-14 

3-32 

3-36 

3-77 

3-75 

3-64 

•227 

1-39 

1-42 

1-41 

1-39 

1-85 

1-61 

171 

•1 

5-60 

3-49 

3-88 

3-78 

•795 

... 

2-45 

... 

2-67 

2'65 

•227 

... 

1-15 

... 

1-30 

... 

1-30 

•05 

5-60 

2-91 

2-95 

3-76 

3-09 

3-02 

3-00 

i     -795    2-08 

2'21 

2-50 

2-16 

2-12 

2-07 

•227       '98 

1-05 

•97 

... 

... 

•96 

•97 

•98 

Concentration  of 
solution. 

E.M.F. 

LiCl. 

LiNO3. 

RbCl. 

RbNO3. 

CsCl. 

CsXOg. 

HCl. 

•5  normal 

5'60 

1-88 

2'28 

•  •  .                             •  •  . 

1-08 

•795 

1-09 

1-59 

•227 

•56 

•89 

... 



... 

•35 

•1 

5'60 

1-29 

1-47 

41-4 

213.0    '  123 

303 

•795 

•87 

•99 

26-4 

82-4        60'5 

115 

•227 

•41 

•53 

11-3 

25-9    i    22-2 

36-6 

•02 

5-60 

14-8 

19-4 

17-6 

20-1 

•795 

... 

... 

9-65 

11-6 

11-7 

13-1 

•227 

4-71 

5-14 

5-9 

6-2 

•004 

5-60 

6-46 

5-44 

7-98 

7-86 

•795 

.  .  . 

... 

4-51 

4-18        5-70 

5-51 

•227 

2-41 

2-26        3-02        2-97 

The  following  table  gives  the  currents  with  TV  normal  solutions 
of  chlorides  and  nitrates  : — 


Chlorides. 

Nitrates. 

E.M.F.      .    . 

5-60 

•795 

•227 

5-60 

•795 

•277 

Caesium    .     . 

123 

60-5 

22'2 

303 

115 

36-6 

Rubidium 

41-4 

26-4 

11-3 

213 

82-4 

25-9 

Potassium 

21-0 

13-4 

5-75 

68-4 

29-3 

9-35 

Sodium     .     . 

3'49 

2-45 

1-15 

3'88 

2-67 

1-32 

Lithium    .     . 

1-29 

•87 

•41 

1-47 

•99 

•53 

Hydrogen      . 

•75 

•27 

94         ELECTRICAL  PROPERTIES   OF  FLAMES 

As  already  mentioned,  Arrhenius  suggested  that  since  all  salts 
of  any  one  metal  give  equal  currents,  they  are  all  converted  into 
hydroxides  by  the  water  vapour  in  the  flame.  On  this  view,  the 
later  experiments  indicate  that  at  the  higher  concentrations  the 
conversion  into  hydroxides  is  not  complete. 

The  conductivity  of  salt  vapours  in  a  current  of  air  was 
measured  by  the  writer  in  1901.1  The  apparatus  used  is  shown 
in  Fig.  25. 


FIG.  25. 

» 

It  consisted  of  a  platinum  tube  TT,  37  cms.  long  and  075  cm. 
in  diameter,  having  a  narrow  tube  T  joined  at  one  end,  and  a 
flange  FF,  6  cms.  in  diameter,  joined  on  at  the  other.  This  tube 
was  supported  horizontally  in  a  Fletcher's  tube  furnace,  the  fire- 
clay blocks  of  which  are  shown  by  the  dotted  lines.  The  flange 
served  to  keep  the  furnace  gases  from  the  open  end  of  the  tube. 
An  electrode,  EE,  consisting  of  a  platinum  tube,  12  cms.  long  and 
0'3  cm.  in  diameter,  was  supported  on  an  adjustable  insulated 
stand,  along  the  axis  of  the  tube  TT.  The  end  of  this  electrode 

1  Phil.  Trans.  A.  vol.  197,  p.  415,  1901.     Phil.  Mag.,  August  1902. 


CONDUCTIVITY   OF   SALT   VAPOURS 


95 


was  closed  by  a  conical  platinum  cap,  which  was  about  9  cms. 
down  the  tube  TT.      ; 

At  T'  the  platinum  tube  was  sealed  on  to  a  glass  tube,  through 
which  the  air  charged  with  spray  entered.  The  spray  was  pro- 
duced by  a  Gouy  sprayer,  S,  which  projected  the  spray  into  a 
glass  bulb,  G,  about  8  cms.  in  diameter,  from  which  the  air  and 
spray  were  led  through  an  inverted  U-tube,  in  which  the  coarser 
spray  settled. 


Kl 


600 


700 


600 


900  1000 

FIG.  26. 


HOO 


1200 


1300 


1400 


The  salt  solution  was  contained  in  a  reservoir  R,  the  level  of 
the  surface  of  the  solution  being  30  cms.  above  the  nozzle  of  the 
sprayer.  The  greater  part  of  the  spray  settled  in  the  bulb  and 
first  half  of  the  U-tube,  and  was  returned  to  R  through  a  tube, 
DD,  up  which  the  liquid  was  forced  by  air  introduced  by  the 
tube  R.  The  supply  of  compressed  air  used  was  obtained  by 
means  of  two  water  injector  pumps.  The  air  pressure  at  the 
sprayer  was  measured  by,  means  of  the  water  manometer  M. 


96 


ELECTRICAL  PROPERTIES   OF   FLAMES 


The  temperature  of  the  tube  was  measured  by  means  of  a 
platinum  platinum-rhodium  thermocouple. 

The  following  table  gives  the  currents  observed  with  a  one 
per  cent,  solution  of  caesium  chloride  at  1340°  C. : — 


P.D.  volts. 

Current  ( 
Outer  tube-. 

amperes). 
Inner  tube  —  . 

1200 

8-8  x 

io-4 

151  x 

io-4 

800 

87 

13-1 

600 

8-8 

9'3 

400 

7'6 

5) 

4-3 

200 

2-3 

H 

1-1 

120 

0-9 

» 

0-5 

J) 

40 

0-2 

j) 

0-1 

?> 

These  results  are  typical  of  the  behaviour  of  most  alkali  salts. 

Fig.  26  shows  the  variation  of  the  current  with  the  temperature 
in  several  cases. 

It  was  found  that  above  800  volts  the  current  was  nearly 
saturated  in  nearly  all  cases,  and  also  that  above  1400°  C.  the 
current  was  nearly  independent  of  the  temperature.  It  appeared, 
therefore,  that  there  was  a  maximum  possible  current  which  could 
not  be  increased  by  raising  either  the  P.D.  or  the  temperature. 

The  table  on  p.  97  gives  the  values  found  for  this  maximum 
possible  current. 

It  is  clear  that  the  maximum  current  is  proportional  to  the 
strength  of  the  solution  sprayed,  and  inversely  proportional  to 
the  electro-chemical  equivalent  of  the  salt. 

Let  M  denote  the  mass  of  salt  entering  the  tube  per  sec.  and  Q 
the  total  charge  on  all  the  positive  or  negative  ions  formed  from 
this  amount  of  salt.  Then  it  appears  from  the  above  results  that 

Q  =A 
M      E 

where  A  is  a  constant  and  E  denotes  the  electro-chemical  equivalent 
of  the  salt. 

According  to  Faraday's  laws  of  electrolysis,  one  gram-equivalent 
of  any  salt  in  the  liquid  state  is  electrolysed  by  the  passage  of 

96,440  coulombs,  or 

Q  _  96,440 
M          E 


CONDUCTIVITY   OF  SALT  VAPOURS 


97 


Salt. 

Grams 
per  litre. 

Electro- 
chemical 
Equivalent. 
E. 

Current. 
C. 

EC. 

CsCl       .      .     . 

10 

168 

15-1x10-4 

2-54x10-1 

Rbl  .     .     .     . 

10 

212 

13-5     „ 

2-86     „ 

KI    .     .     .     . 

10 

166 

16-4     „ 

2-72     „ 

Nal  . 

10 

150 

16'4     „ 

2-46     „ 

CsCl      .     .     . 

1 

168 

1-61  „ 

2-70x10-2 

CsgCOg  .     .     . 

1 

163 

1-61  „ 

2-62     „ 

Rbl  .... 

1 

212 

1-25  „ 

2-65     „ 

RbCL     .     .     . 

1 

121 

2-24  „ 

2-71     „ 

Rb2C03.     .     . 

1 

115 

2'44  „ 

2-80     „ 

KI 

1 

166 

1-66  „ 

2-75     „ 

KBr.     .     .     . 

1 

119 

2-13  „ 

2-53     „ 

KF   .     .     .     . 

1 

58 

4-42  „ 

2-57     „ 

K2C03  . 
Nal  .... 

69 
150 

4-00  „ 
1-82  „ 

2-76     „ 
2-73     „ 

NaBr     .     .     . 

103 

2-44  „ 

2-52     „ 

NaCl     .     .     . 

59 

4-73  „ 

279     „ 

Na2CO.,.     .     . 
Lil   .... 

1 

53 

134 

4-73  „ 
2-03  „ 

2-51     „ 

2-72     „ 

LiBr.     .     . 

1 

87 

3-12  „ 

2-72    „ 

LiCl.     .     .     . 

1 

43 

6-25  „ 

2-69     „ 

Li9C03  .     .     . 

1 

37 

7-48  „ 

2-77     „ 

where  Q  is  the  quantity  of  electricity  required  to  electrolyse  a 
mass  M  of  the  salt. 

The  amount  of  salt  entering  the  tube  was  estimated  by  burning 
the  air  and  spray  along  with  coal  gas,  so  as  to  give  a  Bunsen 
flame.  An  equal  flame  was  arranged  near  the  first  one,  in  which 
a  bead  of  salt  on  a  platinum  wire  could  be  placed.  By  adjusting 
the  position  of  the  bead  it  was  possible  to  arrange  so  that  the  two- 
flames  were  equally  brightly  coloured  by  the  salt.  The  loss  of 
weight  of  the  bead  in  a  known  time  then  gave  the  amount  of 
salt  passing  through  the  tube.  This  method  was  first  used  by 
Arrhenius.1  In  this  way  it  was  found  that  when  a  solution 
containing  one  gram  per  litre  was  sprayed,  27  x  10 ~r  grams  of 
salt  entered  the  tube  per  second. 

1  Wied.  Ann.  vol.  xlii.  p.  18,  1891. 


98 


ELECTRICAL  PROPERTIES   OF  FLAMES 


Hence  we  get 

EQ  _  2-63  X  IP'2  " 
"  "M"     2-70  x  10-' 

This  agrees  as  well  as  could  be  expected  with  the  value  96,440 
found  for  solutions.  It  appears,  therefore,  that  Faraday's  laws  of 
electrolysis  of  liquids  apply  also  to  salts  in  the  state  of  vapour. 
In  other  words,  Q/M  is  the  same  in  salt  vapours  at  1400°  C.  as  in 
solutions  at  the  ordinary  temperature. 

Since  equivalent  weights  of  the  alkali  salts  contain  equal 
numbers  of  metal  atoms,  it  follows  that  the  charge  carried  by 
the  salt  vapours  per  atom  of  metal  is  the  same  a*s  the  charge  on 
one  monovalent  ion  in  solutions. 

The  ratio  of  the  charge  e  to  the  mass  m  for  the  positive  ions 
of  alkali  sulphates  has  recently  been  determined  by  O.  W.  Richard- 
son,1 by  observing  their  deflection  in  a  magnetic  field.  The  method 
used  was  the  same  as  that  described  in  Chap.  V  for  the  positive 
ions  emitted  by  a  hot  strip  of  platinum.  The  hot  strip  was  coated 
with  the  alkali  sulphate.  The  following  table  gives  the  mean 
values  of  e/m  found  by  Richardson. 

Since  in  the  electrolysis  of  solutions  one  gram  of  hydrogen  is 
deposited  by  the  passage  of  9644  electromagnetic  units  of  electricity, 
we  have  e/m  for  a  hydrogen  atom  in  solutions  equal  to  9644.  If 
we  divide  9644  by  the  values  of  e/m  found  for  the  positive  ions, 
we  get  their  equivalent  weights. 


Substance. 

e/m. 

Equivalent  weights 
of  +  ions. 
(H  =  1). 

Atomic  weights  of 
metals. 

Li2S04     .... 

1600 

6-0 

7-0 

Na2SO4    .... 

430 

22*5 

23-1 

K2S04     .... 

265 

36-4 

39-2 

Kb2SO4    .... 

101 

96 

85-4 

Cs2SO4     .... 

73 

132 

133 

It  is  clear  from  these  results  that  the  positive  ions  emitted  by 
the  alkali  sulphates  at  high  temperatures  contain  the  metal  only, 


1  Phil.  Mag.,  December  1910. 


CONDUCTIVITY   OF   SALT   VAPOURS  99 


• 


and  that  the  charge  per  atom  of  metal  is  the  same  as  in  solutions. 
These  experiments,  however,  give  no  information  as  to  the  number 
of  atoms  of  the  metal  in  each  ion.  As  we  have  seen,  the  positive 
ions  in  flames  are  probably  single  atoms,  so  that  most  likely  the 
same  is  true  in  the  present  case.  Davisson 1  has  made  a  series 
of  measurements  of  e/m  for  the  positive  ions  emitted  by  salts  of 
the  alkaline  earths.  He  found  they  were  single  atoms  of  the 
metal  with  single  ionic  charges  in  most  cases. 


APPENDIX. 


Since  all  alkali  salts  give  positive  ions  having  equal  apparent 
velocities,  Langevin  2  suggested  that  these  ions  consist  of  hydrogen 
atoms.  The  formula  k  =  eh/mv  gives  about  300  for  a  hydrogen 
atom  in  a  flame  at  2000°  C.  This  view  is  supported  by  Lusby 
(loc.  cit.),  who  finds  7^  =  300.  I  think  Lusby 's  value  is  too  high 
and  prefer  the  explanation  of  the  equality  of  the  velocities  given 
above.  However,  the  question  must  be  regarded  as  an  open  one, 
and  further  experiments  are  required  before  a, 'definite  conclusion 
can  be  arrived  at. 

1  Phil  Mag.,  January  1912. 

2  Comptes  rendus,  t.  CXL.,  1905,  p.  35. 


H  2 


CHAPTER  VIII 

THE  ELECTRICAL   CONDUCTIVITY  OF    FLAMES    FOR 
RAPIDLY  ALTERNATING  CURRENTS 

THE  conductivity  of  flames  for  rapidly  alternating  currents  was 
investigated  by  E.  Gold  and  the  writer.1  The  apparatus  used  is 
shown  in  Fig.  27. 

A  mixture  of  coal  gas  and  air  containing  spray  was  burnt  as 
a  non -luminous  flame,  with  a  sharply  denned  inner  cone.  The 


FIG.  27. 

electrodes  used  were  concentric  platinum  cylinders  5  cms.  high 
and  2'4  and  1'2  cms.  in  diameter. 

The  conductivity  between  the  electrodes  was  determined  by 
means  of  a  Wheatstone-bridge  arrangement,  of  which  the  electrodes 
formed  one  arm,  and  the  other  three  arms  consisted  of  small  air 
condensers,  the  capacity  of  one  of  which  was  adjustable  with  a 
micrometer  screw. 

An  induction-coil,  I,  charged  two  Leyden  jars  J\,  J2,  and  these 

1  Phil.  Mag.,  April  1906. 
100 


ELECTRICAL  CONIJ^OTJVTTY    <W  FLAMES     101 

discharged  at  a  spark  gap  S.  The  outside  coatings  of  the 
jars  were  connected  through  the  primary  of  a  Tesla  coil,  T. 
The  primary  of  this  coil  consisted  of  33  turns  wound  into  a 
spiral,  29  cms.  long  and  19  cms.  in  diameter,  on  a  glass  cylinder. 
The  secondary  coil  had  three  turns,  and  was  placed  inside  the 
glass  cylinder,  half-way  up  it.  It  was  connected  to  the  bridge 
arrangement  at  A  and  B,  as  shown. 

An  "  electrolytic  detector,"  D,  was  connected  to  the  points  M 
and  N  of  the  bridge.  This  detector  consisted  of  two  platinum 
electrodes  dipping  into  20  per  cent,  sulphuric  acid.  One  electrode 
was  a  platinum  cylinder  3  cms.  in  diameter  and  4  cms.  high,  while 
the  other  was  a  platinum  wire  -j^Vo"  inch  in  diameter  sealed  into  a 
glass  tube  and  cut  off  close  to  the  surface  of  the  glass.  The 
two  electrodes  were  connected  to  a  silver-chloride  cell  B  and  a 
galvanometer  G.  The  cell  B  gave  about  one  volt,  and  served  to 
polarize  the  electrodes.  When  an  alternating  P.D.  was  produced 
between  M  and  N  the  detector  was  depolarized  and  a  current 
passed  through  the  galvanometer.  The  condensers  Cx  and  C2  each 
consisted  of  two  parallel  circular  discs,  10  cms.  in  diameter,  well 
insulated.  The  distance  between  the  discs  of  Cj  was  0'15  cm., 
and  of  C2  0'75  cm.,  in  most  of  the  experiments.  The  condenser  C3 
consisted  of  two  discs,  10  cms.  in  diameter,  whose  distance  apart 
could  be  adjusted  and  measured  with  a  micrometer  screw. 

On  working  the  coil  with  the  electrodes  E  in  the  flame,  it  was 
found  that  by  adjusting  the  capacity  of  the  condenser  C3  the 
galvanometer  deflection  could  be  reduced  to  a  very  small  minimum 
value.  This  shows  that  the  electrodes  in  the  flame  for  very  rapidly 
alternating  currents  behave  like  a  capacity  or  a  self-induction,  and 
not  like  a  resistance. 

The  change  in  the  capacity  of  a  parallel  plate  condenser  is  very 
nearly  proportional  to  the  change  in  the  reciprocal  of  the  distance 
between  its  plates.  Thus,  if  d.2  is  the  distance  with  which  the 
bridge  is  balanced  with  a  flame  filled  with  salt,  and  dl  that  for  the 
flame  free  from  salt,  the  d2~l  —  d^~l  is  proportional  to  the  change 
in  the  apparent  capacity  of  the  flame  electrodes  due  to  introducing 
the  salt. 

It  was  found  that  d2~l  —  d^1  was  approximately  independent  of 
the  number  of  alternations  of  the  P.D.  per  sec.  Thus  when  the 


102       ELECTRICAL   PROPERTIES   OF   FLAMES 

number  per  sec.  was  changed  from  7  x  104  to  6  x  106,  d^-1  —  d^ 
changed  from  2'1  to  3'0.  If  we  suppose  the  change  in  dz~l  —  i/^1 
proportional  to  nx,  where  n  is  the  number  of  alternations  per  sec., 
then  this  shows  that  x  is  not  greater  than  0'05.  For  a  pure 
capacity  x  =  0,  and  for  a  pure  self-induction  x  =  1,  so  that  it_ 
appears  that  the  flame  behaves  nearly  like  a  pure  capacity. 

The  variation  of  d2~l  —  dt~l  with  the  P.D.  at  constant  frequency 
was  examined,  and  it  was  found  to  be  nearly  inversely  proportional 
to  the  square  root  of  the  P.D. 

With  parallel  plate  electrodes,  d2-l  —  dl~l  was  nearly  independent 
of  the  distance  between  the  electrodes. 


THEORY  OF  THE  CONDUCTIVITY  FOR  RAPIDLY  ALTERNATING 

i 

CURRENTS. 

Suppose  a  large  parallel  plate  condenser  filled  with  a  uniformly 
ionized  gas,  and  let  the  distance  between  the  plates  be  D  cms. 
Let  the  potential  difference  between  the  plates  be  given  by  the 
formula  V  =  V0  sm  pt,  and  let  the  number  of  positive  or  negative 
ions  per  c.c.  be  n,  each  ion  carrying  a  charge  +  e.  In  a  Bunsen 
flame,  the  velocity  of  the  negative  ions  is  about  one  hundred  times 
that  of  the  positive  ions,  and  the  mass  of  the  positive  ions  is  very 
large  compared  with  that  of  the  negative  ions,  so  that  in  a 
rapidly  alternating  electric  field  the  amplitude  of  vibration  of 
the  negative  ions  must  be  very  large  compared  with  that  of  the 
positive  ions. 

For  an  approximate  calculation,  therefore,  we  may  assume  that 
the  positive  ions  do  not  move,  so  that  all  the  current  is  carried  by 
the  negative  ions.  Also,  let  us  suppose  that  all  the  negative  ions 
move  in  the  same  way,  with  the  same  velocity,  so  that  the  number 
of  negative  per  c.c.  remains  n  except  within  a  distance  d  of  each 
electrode,  d  being  twice  the  amplitude  of  vibration  of  the  negative 
ions.  It  is  easy  to  see  that  on  these  assumptions  the  negative 
ions  will  practically  all  be  contained  in  a  slab  of  thickness  D  —  d, 
which  will  vibrate  between  the  plates  so  as  just  not  to  touch  either 
of  them.  For  if  a  new  negative  ion  is  formed  outside  the  slab  it 
will  almost  immediately  strike  the  electrode  near  it;  whereas  a 
new  negative  ion  formed  in  the  slab  cannot  reach  either  electrode, 


ELECTRICAL  CONDUCTIVITY  OF   FLAMES     103 

except  by  diffusion,  which  we  shall  neglect.  Thus  we  may  regard 
the  whole  space  between  the  plates  as  filled  with  positive  electricity 
of  density  +  ne,  and  the  vibrating  slab  of  thickness  D  —  d  as 
containing  also  negative  electricity  of  density  —  ne.  Thus  inside 
the  slab  the  total  density  is  zero,  and  outside  is  +  ne. 

Let  X  denote  the  electric  intensity  between  the  plates  at  a 

distance   x   from  one  of  them.     Then,  inside  the  slab      j-  =  0, 

and  outside  -5-  =  4mne. 
ax 

Let  A  and  B  (Fig.  28)  be  the  two  plates,  and  let  the  slab  be 
represented  by  the  space  between  the  two  dotted  lines  E,  F.     Let 


V, 


B 


FIG.  28. 


AB  =  D,  AE  =  tv  FB  =  t.2,  and  suppose  the  potential  of  A  kept 
zero,  while  that  of  B  =  V.  Let  the  rise  of  potential  in  AE  be  V1, 
in  EF  be  V3,  and  in  FB  be  V2.  In  EF  let  X  =  X0.  Then 


V3  =  —  X0(D—  d\  where  d  =  tl-\-  t2.     In  AE  we   have  -y-r  — 


—  4tfrp,    where   p  =  ne.      From   this   we   get   —  =  —  4>7ipx  +  C 

cix 

and  V  =  —  27CQX2  -f-  Cx  +  D,  where  C  and  D  are  constants  to  be 
determined.     When  x  =  0,  V  =  D  =  0,  and  when  x  =  tt— 


Hence—  Vl  = 

In  the  same  way  in  FB  we  have 

V  =  -  2npx2  +  C'x  +  D'. 


104       ELECTRICAL  PROPERTIES   OF  FLAMES 

^7V 
When  x  =  D  -  t2    ^  =  -  X0  and  V  =  V,  +  V8; 

so  that  we  get  for  V  at  x  =  D  — 


Now  ^  +  t2  =  d,  so  that 

V  =  -  X0D  +  Znpdtft!  -d)    .....     (1) 


The  force  acting  on  a  negative  ion  is  —  X0e  —  A^,1,  where  A  is  a 

constant  representing  the  viscous  resistance  to  motion  with  unit 
velocity.  Let  m  be  the  mass  of  a  negative  ion  ;  then  its  equation 
of  motion  is 

v  dHi  ,    \dti 

-X0e=m^  +  A^  .......     (2) 

The  current  density  inside  the  slab  is  given  by  the  equation  — 

dL       K  dX 


where  K  is  the  specific  inductive  capacity  of  the  medium  between 
the  plates  in  the  absence  of  ions.     Thus,  K  is  unity,  and 


Now,  in  a  flame  containing  a  salt  vapour,  the  fall  of  potential 
nearly  all  takes  place  near  the  electrodes,  so  that  X0  is  probably 
very  small,  even  when  rapidly  alternating  currents  are  used.  Con- 

sequently, since  Q  is  large,  —  --  -^-  may  be  neglected  in  comparison 

with  —  Q  -^  •      Hence  (3)  becomes  i  =  —  Q  ~~  approximately. 
Substituting  in  (1)  the  value  of  X0  got  from  (2),  we  get 
V  =  YoSin^  =  D(^5  +  ^f) 

This  gives 

mD  d\       AD  d\ 

~ 


-D   , 

But  -TT  =  ---  Hence  — 

dt  Q 

mD  dzi    ,   AD  di 
^  ^  +  —  jt 


ELECTRICAL  CONDUCTIVITY   OF   FLAMES      105 

The  solution  of  this  equation  is 


i  =  _  w -pp-        ....     (5) 

1  \        p2mT)/  m2J 

where 


/ 
tana  = 


A 

If  a  P.D.  V  =  V0sin^  is  applied  to  a  condenser  of  capacity  C, 
the  current  is  given  by  the  equation  i  =  CV0p  cospt.  For  the 
flame,  if  A  and  m  are  both  negligible,  (5)  becomes 


4>nd 
so  that  the  apparent  capacity  is    -—  per  unit  area.     Now      is  the 


amplitude  of  vibration  of  the  negative  ions,  so  that  qd  must  be  the 
amount  of  electricity  flowing  during  a  half  vibration. 

Let  i  =  --    t  so  that  Q  =  ^~  sin^.    Then  we  have,  integrat- 
ing from  0  to  n, 


y 

Qd  =  ^  or  ^  = 


so  that  the  apparent  capacity  per  unit  area  is 


1  /    g 


If  Q  =  0   this   makes   the   capacity   zero,   whereas   it   should 

T  1       ^J"V 

v~-ri  *     This  is  due  to  the  omission  of  -       7,°,  which  would  not 
In!)  4>n  at 


be  negligible  if  £  were  small.      If,  however,  we  take  A/      ^    to  be 

the  increase  in  the  apparent  capacity  due  to  the  presence  of  the 
ions,  then  no  error  will  be  made,  even  if  Q  be  small. 

According  to  the  theory,  therefore,  we  should  expect  the 
apparent  capacity  to  be  independent  of  the  number  of  alternations 
per  second,  and  of  the  distance  between  the  electrodes,  and  to  be 
inversely  proportional  to  the  square  root  of  the  potential  difference 


106       ELECTRICAL   PROPERTIES   OF  FLAMES 


between  the  electrodes,  which  agrees  exactly  with  the  experimental 
results. 

The  expression  ^J     ^,    has  been  obtained  by  neglecting  the 


mass  of  the  negative  ions,  and  the  resistance  to  their  motion,  so 
that  it  appears  that  the  alternating  current  through  the  flame  is 
determined  merely  by  the  density  of  the  layer  of  positive  charge 
left  in  the  gas  near  the  electrodes  when  the  negative  ions  move 
under  the  action  of  the  alternating  electric  field. 


KtV 


JO 


50         60          70 

FIG.  29. 


If  a  steady  P.D.  is  applied  to  two  electrodes  immersed  in  an 
ionized  gas,  and  if  the  positive  ions  cannot  move,  it  is  easy  to  see 
that  a  current  will  only  pass  for  the  short  time  required  for  the 
accumulation  of  a  positive  charge  near  the  negative  electrode  to 
become  sufficient  to  make  the  electric  force  near  the  positive 
electrode  zero.  Thus  the  two  electrodes  will  behave  like  a  con- 
denser when  the  P.D.  is  applied.  When  a  rapidly  alternating  P.D. 
is  applied  it  is  easy  to  see  that  even  if  the  positive  ions  move,  pro- 
vided their  velocity  is  small  compared  with  that  of  the  negative  ions, 
the  arrangement  will  behave  like  a  condenser  if  the  number  of  ions 
per  c.c.  is  very  large,  and  the  mass  of  the  negative  ions  very  small. 


ELECTRICAL  CONDUCTIVITY  OF  FLAMES     107 

The  following  table  gives  the  values  found  for  d2~l  —  d^1  with 
a  number  of  salt  solutions  sprayed  into  the  flame  : — 


Salt. 

Grams  per  litre. 

du 

(in  tenths  of  an  inch). 

i       i 

(«2        di 

CsCl  . 

50 

0'08 

12-2 

10 

0-18 

5-26 

55           

1 

0-34 

2-64 

0-333 

0-48 

1-78 

O'l 

1-10 

0-61 

Cs2C03    .... 

25-5 

0-13 

7'40 

??     

2-55 

0-30 

3-03 

5)          

0-26 

0-59 

1-40 

35          

0-026 

1-90 

0-23 

RbCl 

48-1 

0'22 

4'24 

9'6 

0'29 

3'15 

,,     .     .     .     .     • 

1-92 

0'41 

2-14 

Rb2C03  .... 

50-4 

0-19 

4-96 

10 

0-25 

3-70 

>}    •     •     •    •  -  • 

1 

0-50 

1-70 

K2C03    .    ;;"':.. 

100 

0-062 

15-8 

3)         .         •         •         •         • 

10 

0-297 

3-07 

KC1   .     .    ,  •.    . 

100 

0-20 

4-70 

20'8 

0'30 

3  -03 

1 

0-50 

1-70 

NaCl 

100 

0'47 

1*83 

LiCl  

102-5 

1-3 

0-47 

In  Fig.  29  the  above  values  of  d2~l— d^1  are  shown  graphically. 
Fig.  30  shows  the  steady  currents  due  to  an  E.M.F.  of  0*227  volt, 
between  cylindrical  electrodes  in  a  flame,  taken  from  the  paper  by 
Smit hells,  Dawson  and  the  writer  (see  p.  92). 

The  amount  of  salt  entering  the  flame  per  second  was  nearly 
the  same  in  the  two  sets  of  experiments. 

The  following  table  gives  the  values  of  d.2  ~ 1  —  d^1  for  decinormal 
solutions  obtained  from  the  curves  in  Fig.  29,  and  also  the  steady 
currents  due  to  0'227  volt : — 


108       ELECTRICAL   PROPERTIES   OF  FLAMES 


Salt. 

i      i 

V1 

Salt. 

Steady  Current. 
(1  =  10  -7  ampere). 

Ratios. 

V*' 

"    k  ' 

CsCl   .     .    . 

6-7 

CsCl  .     .    . 

22-2 

3'3 

0-70 

£Cs2C03    .     . 

5-9 

CsN03 

36-6 

6'2 

1-03 

iRb2C03   .     . 

3-7 

RbN03  .    . 

25-9 

7 

1-37 

RbCl  .     .    . 

3-2 

RbCl     .    . 

11-3 

3-5 

1-05 

£K2C03     .    . 

2-9 

|K2C03  .     . 

11-2 

3-9 

1-15 

KC1    .     .     . 

2-6 

KC1  .    .    . 

5-75                2-2 

0-92 

In  the  work  with  steady  currents  the  conductivities  of  caesium 
and  rubidium  carbonates  were  not  measured ;  so  the  values  for 
nitrates  are  given,  since  the  conductivities  of  all  oxysalts  of  the 
same  metal  were  found  to  be  nearly  equal  for  steady  currents. 


40 


30 


rii  ^o 

I 
6    10 


TGPt 


0  10  20     C,?/)MS  P£ft  LtTffZ 

FIG.  30. 

The  last  column  contains  the  square  root  of  the  conductivity  for 
steady  currents  divided  by  d2  ~ l  —  d^  ~ l.  The  numbers  in  this  column 
do  not  vary  much,  which  shows  that  the  conductivity  for  rapidly 
alternating  currents  varies  nearly  as  the  square  root  of  the 
conductivity  for  steady  currents. 

The  conductivities  of  potassium  chloride  and  rubidium  chloride 
were  found  to  vary  nearly  as  the  square  root  of  the  concentration 


ELECTRICAL   CONDUCTIVITY   OF  FLAMES      109 

for  steady  currents  ;  so  that  we  should  expect  them  to  vary  as  the 
fourth  root  of  the  concentration  for  rapidly  alternating  currents 
and  this  was  found  to  be  approximately  true.1 

The  steady  currents  due  to  0'227  volt  are  probably  proportional 
to  the  number  of  ions  present  per  c.c.  in  the  flame,  so  that  the 
comparison  of  the  conductivities  for  steady  and  alternating  P.D.'s 
shows  that  for  the  latter  the  conductivities  as  measured  by 
d2~l  —  6?1"1  are  proportional  to  the  square  root  of  the  number  of 
ions  present  per  c.c.  This  is  what  we  should  expect  from  the 


formula  A/,    ^  ,  for  Q  =  ne. 


It  appears,  therefore,  that  the  theory  considered  agrees  very 
well  with  the  facts. 

If  c  denotes  the  increase  in  the  apparent  capacity  per  unit 
area,  we  have 

~V       K-l 


where  K  is  the  apparent  specific  inductive,  capacity  of  the  salt 

V  (K  —  I)2 
vapour.     Hence  Q  =  -°^  ,^ — •  '   With  air  between  the  electrodes 

instead  of  flame,  d  was  equal  to  6'66,  while  with  the  flame  free 

(*.($(* 

from  salt,  it  was  3'33.     Hence  K  =  — - j—  very  nearly. 

a2 

The  table  on  p.  110  gives  a  few  values  of  K.  K,  of  course, 
has  no  relation  to  the  true  specific  inductive  capacity  of  the 
salt  vapours,  which  must  be  little  different  from  unity.  The  third 
column  contains  the  values  of  the  number  of  ions  per  c.c  given  by 

V  (K  —  I)2 

the  equation  ne  =    °^  ,-.2      •    V0  was  about  1'2  E.S.  units,  and  D 

was  0*6  cm.     e  was  taken   to   be  5  x  10  ~10  E.S.  units,  so   that 
n  =  1-06  x  109(K  -  I)2. 

The  amount  of  salt  entering  the  flame  per  minute  when  a 
solution  containing  one  gram  per  litre  was  sprayed  was  0'053 
milligram.  The  velocity  of  the  flame  gases  was  about  200  cms. 
per  sec.,  and  the  diameter  of  the  flame  about  3  cms.,  so  that  the 

1  H.  A.  Wilson  and  E.  Gold  (loc.  cib.\ 


110       ELECTRICAL  PROPERTIES   OF  FLAMES 


Salt. 

Grams  per 
litre. 

K. 

n. 

N. 

08,06, 

25-5 

51 

2-7  x  1012 

5-5  x  1013 

» 

2-55 

22 

-      4-7  x  1011 

5-5  x  1012 

ij 

0-26 

11 

1-1  x  1011 

5-6  x  1011 

CsCl 

0-026 
50 

3-5 

83 

6-7  x  109 
7-2  x  101- 

5-6  x  1010 
101* 

» 

10 

37 

1-4  x  1012 

2      x  1013 

)» 

1 

20 

3-9  x  1011 

2      x  1012 

RbCl 

01 

48-1 

6 
30 

2-7  x  1010 
9     x  1011 

2      x  1011 
1-4  x  1014 

?> 

1-92 

16 

2-4  x  1011 

5-6  x  1012 

K2C03 

100 

107 

1-3  x  1013 

5-1  x  1014 

»• 

10 

22 

4-7  x  1011 

5-1  x  10™ 

KC1 

100 

33 

1-1  x  1012 

4-7  x  1014 

» 

20-8 

22 

4-7  x  1011 

9-7  x  1013 

>j 

1 

12 

1-3  x  1011 

4-7  x  1012 

NaCl 

100 

14 

1-8  x  1011 

5-9  x  1014 

LiCl 

102-5 

5 

1-7  x  1010 

8-4  x  1014 

Free  flame 

— 

2 

1-1  x  109 

amount  of  salt  per  c.c.   in  the  flame  was  about   G  x  6  x  10~7 
milligram  with  a  solution  containing  G  grams  per  litre. 

Let  N  denote  the  number  of  metal  atoms  per  c.c.,  and  E  the 
chemical  equivalent  of  the  salt.     Then 

G  x  9644  x  3  x  1010  x  6  x  1Q-10      G 

E 
9644 


N  = 


=  ~  x  3-5  x  1014 


5  x  10-10  x  E 
for  ~w~  is  the  number  of  metal  atoms  in  one  gram  of  the  salt. 

The  last  column  in  the  above  table  contains  the  values  of  N 
given  by  this  formula. 

It  will  be  seen  that  with  the  dilute  solutions  of  caesium  salts 
the  number  of  ions  is  about  one-tenth  the  number  of  metal  atoms 
present.  With  salts  of  the  other  metals  the  proportion  of  ions 
is  less.  The  values  of  n  and  N,  of  course,  are  subject  to  a 
large  possible  error.  For  caesium  salts  at  very  small  concentrations 
it  seems  probable  that  n  and  N  do  not  really  differ  very  much. 

We  can  get  a  rough  estimate  of  the  velocity  of  the  negative  ions  *• 
in  the  flame  without  salt  by  using  the  value  of  n(=  1*1  X  109) 
and  the  known  conductivity  of  the  flame  for  steady  currents.  We 


1  E.  Gold,  Proc.  Ray.  Soc.  A.  vol.  79,  p.  43,  1907. 


ELECTRICAL  CONDUCTIVITY   OF   FLAMES      111 


have  i  =  JLne(k1+kz)&nd       =  10'15  E.M.  units,1  e  =  17  X  1Q 


-20 


Hence  7^  +  k2  =  5'3  X  10  ~5.  But  7^  is  small  compared  with  kz, 
so  that  for  one  volt  per  cm.  we  get  7,\2  =  5300.  This  agrees  as 
well  as  could  be  expected  with  the  theoretical  value  for  a  negative 
electron. 

1  See  p.  62. 


CHAPTER   IX 
FLAMES   IN   A  MAGNETIC   FIELD 

IT  will  be  convenient  to  begin  by  considering  the  theory  of 
the  effect  of  a  magnetic  field  on  a  flame.  Suppose  that  a  thin 
plane  vertical  sheet  of  flame  moving  upwards  with  velocity  V  is 
acted  on  by  a  magnetic  force  of  strength  H  perpendicular  to  the 
sheet.  Let  there  be  a  vertical  uniform  electric  field  of  strength  Y 
upwards  in  the  flame. 

Since  the  velocity  of  the  negative  ions  is  very  large  compared 
with  that  of  the  positive  ions,  only  the  former  need  be  considered. 
The  equations  of  motion  of  a  negative  ion  describing  a  free  path 
are 

d2x  dy 

m-Td  =  Xe  —  He~~ 

dt2  dt 

d2y      „        TT  dx 

m:dr=  ^  +  He-r- 
dt2  dt 

d2z      „ 
mdf*=* 

where  y  is  measured  vertically  upwards,  and  x  horizontally  at 
right  angles  to  the  magnetic  field. 

If  we  regard  the  gas  as  a  viscous  medium,  exerting  a  force 
on  the  ions  proportional  to  their  velocity,  the  equations  of  motion 
become 

d2x      v        TT  <%       e  dx 

m-r^  =  Xe  —  He  -£  —  77-  -TT 

dt2  dt      kz  dt 


dt2  dt      k't\dt 

d2z  e  dz 

m<P=    ~%M 

where  k9'  is  the  value  of  &2  in  the  magnetic  field,  and  differs 

slightly  from  k2. 

112 


FLAMES   IN  A  MAGNETIC  FIELD  113 

In  a  steady  state,  therefore,  putting  u  =  ^,  v  =  -^,  we  get 
X  =  H*  +  £ 

A/2 

Y=  -H^  +  'T^- 


If  the  sides  of  the  flame  are  insulated  the  velocity  u  must  be 
zero,  since  there  can  be  no  horizontal  current  ;  so  that 

X  =  Ht? 

*-V 


which  give  X  -  HV  =  fc2TH. 

If  the  top  and  bottom  of  the  flame  are  insulated  the  upward 
velocity  of  the  negative  ions  must  be  equal  to  that  of  the  positive 
ions,  which  move  with  the  flame,  so  that  — 

X  =  HV  +  " 

#2 

Y  =  -  H.U, 
which  give  Y  =  -  &2/H(x  -  HV)- 

If  Y  is  one  volt  per  cm.,  or  108,  &2'Y  is  about  104;  so  that  V, 

c*m 
which  is  about  200  —  —  ',  can  be  neglected  compared  with  &2'Y. 

In  the  above  I  have  assumed  that  X  and  Y  are  uniform.  The 
transverse  stream  of  negative  ions  requires  an  excess  of  ionization 
over  recombination  along  one  side  of  the  flame,  and  an  equal 
excess  of  recombination  along  the  other.  Consequently,  near  the 
edges  X  and  Y  will  not  be  uniform,  but  a  little  way  from  the 
edges  the  ionization  and  recombination  will  be  equal,  and  X  and 
Y  uniform.  In  measuring  X  or  Y  it  is,  consequently,  necessary 
to  measure  the  P.D.  between  wires  put  in  a  little  way  from  the 
edges  of  the  flame.  Near  the  electrodes  used  to  produce  the 
field  it  will  not  be  uniform,  so  that  these  electrodes  ought  to 
be  some  distance  from  the  place  where  the  transverse  field  is 
measured. 

The  condition  that  the  sides  of  the  flame  be  insulated  is 
difficult  to  fulfil  in  practice.  For  example,  if  a  small  flat  flame 
is  placed  between  the  poles  of  a  magnet,  so  that  the  top  and 


114       ELECTRICAL  PROPERTIES   OF  FLAMES 

bottom  of  the  flame  are  in  a  weaker  field  than  the  middle,  the 
charges  corresponding  to  the  induced  field  X  can  leak  across  the 
top  and  bottom  of  the  flame.  In  consequence,  the  actual  value  of 
X  will  be  less  than  that  calculated.  If  horizontal  electrodes  are 
put  in  the  flame  they,  connect  together  the  sides,  and  so  must 
greatly  diminish  X.  To  get  the  full  theoretical  value  of  X  it  is 
necessary  that  the  length  of  flame  in  the  magnetic  field  should 
be  large  compared  with  the  breadth  of  the  flame,  and  also 
that  the  horizontal  electrodes  should  be  a  long  way  from  the 
place  where  X  is  measured.  These  conditions  have  to  be  satisfied 
in  measuring  the  Hall  effect  in  a  thin  metal  plate,  as  is  well 
known. 

The  Hall  effect  in  Bunsen  flames  has  been  examined  by 
E.  Marx.1  He  -used  a  small  flat  flame  between  the  poles  of  a 
magnet.  The  electrodes  were  horizontal  gratings,  through  which 
the  flame  passed.  Unfortunately  these  electrodes  seem  to  have 
only  been  two  or  three  cms.  apart,  while  the  breadth  of  the  flame 
was  also  about  two  or  three  cms.  Consequently,  the  sides  of  the 
flame  were  really  connected  together  by  the  electrodes,  instead 
of  being  insulated.  Consequently  the  values  found  for  the  trans- 
verse electric  force  must  be  much  smaller  than  the  theoretical 
value. 

The  horizontal  electric  field  X  was  measured  by  two  wires 
connected  to  a  quadrant  electrometer. 

The  following  table  gives  some  of  the  value  found  for  X/HY 
with  potassium  chloride  solutions  sprayed  into  the  flame  : — 


Concentration  of  Solution. 

X/HY. 

0 

-  10-18  x  10-6 

0*125  normal 

-    8-24       ,, 

0*5 

-    4*26       ,, 

2*0 

-    3-78       ,, 

3*8 

-    3-75       ,, 

For  strong  solutions  X/HY  was  nearly  independent  of  the 
concentration. 

1  Ann.  der  Physik,  Band  2,  1900. 


FLAMES   IN  A  MAGNETIC  FIELD  115 

The  following  table  gives  the  values  found  with  strong  solution 
of  salts  of  all  the  alkali  metals  : — 


Metal. 

XHY. 

0<i6siiini 

-  172  x 

10-6 

Rubidium 

-  2-7 

Potassium 

-  3-72 

Sodium      
Lithium    . 

-  5-06 

-  7-86 

99 

These  numbers  are  nearly  inversely  proportional  to  the  square 

roots  of  the  atomic  weights  of  the  metals. 

v 
We  have  &2'  =  YTT?  X  108  for  one  volt  per  cm.  approximately, 

for  HV  is  small  compared  with  X.  Marx's  results,  therefore, 
indicate  values  of  lc\  varying  from  1018  for  the  flame  without 
salt,  down  to  172  for  caesium  salts.  If  the  negative  ions  are  free 
electrons,  which  is  probable,  k'2  ought  to  be  about  20,000.  The 
short-circuiting  of  the  sides  of  the  flame  by  the  horizontal  electrodes 
probably  explains  the  low  values  found  for  X/HY  and  the  variation 
of  it.  The  values  found  are  lower  the  greater  the  conductivity  of 
the  flame,  which  is  what  we  might  expect.  Consequently,  these 
experiments  do  little  more  than  indicate  that  the  Hall  effect 
exists,  and  is  in  the  direction  to  be  expected  from  the  fact  that 
/J2  is  much  greater  than  &r 

Some  measurements  of  the  Hall  effect  made  under  my  direction 
a  few  years  ago,  but  not  hitherto  published,  indicated  a  value  of 
X/YH  about  ten  times  that  found  by  Marx  for  the  flame  free 
from  salt.  In  these  experiments  care  was  taken  to  have  the 
horizontal  electrodes  sufficiently  far  from  the  place  where  X  was 
measured.  These  experiments  gave  k.2  equal  to  about  10,000r 
which  is  of  the  order  of  magnitude  to  be  expected  for  free 
electrons. 

The  effect  of  a  magnetic  field  on  the  conductivity  of  the  Bunsen 
flame  was  examined  by  the  writer.1  The  flame  used  consisted  of 
a  row  of  twelve  small  Bunsen  flames,  burning  from  quartz  tubes. 

1  Proc.  Roy.  Soc.  A.  vol.  82,  1909. 


116       ELECTRICAL  PROPERTIES   OF  FLAMES 


These  gave  a  flame  about  14  cms.  long,  6  cms.  high,  and  2  cms. 
thick. 

A  current  was  passed  horizontally  along  the  flame  between 
two  platinum  electrodes,  and  the  uniform  potential  gradient 
between  the  electrodes  was  measured  by  means  of  two  exploring 
wires  7  cms.  apart,  connected  to  an  electrostatic  voltmeter. 

The   flame  was  placed  between  the  poles  of  a  large  electro- 


—  & 

<u 
o 

C    T 

070  
A 

/ 

3 

(0 

A 

I 

gj 

<t  JL 

o-J 

(D 
bO 

*t    — 

t 

O 

*-. 

/, 

0>    | 

txO 

gj 

2 

C    1 

o  1 

/ 

/x 

£< 

J/ 

V 

X 

/ 
/x 

\ 

V 

X 

V 

oo  -5,0 

30  -4,0 

jo-ao 

30  -Zp 
**^min 

30  -U 

5? 

ID 

X)    2X 

00   3^ 

Mdgi 

>00  40QO  5,000  6fH 

ietic  field 

<•) 

© 

X 

\ 

FIG.  31. 

magnet,  which  gave  a  nearly  uniform  field  over  the  entire  area  of 
the  flame  between  the  exploring  wires. 

Some  potassium  carbonate  was  put  on  the  negative  electrode 
to  diminish  the  drop  of  potential  there,  and  so  increase  the  cur- 
rent. There  was  no  salt  in  the  part  of  the  flame  between  the 
poles  of  the  magnet.  The  ratio  of  the  potential  difference  between 
the  exploring  wires  to  the  current  was  taken  as  a  measure  of  the 
resistance  of  the  flame. 

Fig.  31  shows  the  results  obtained. 


FLAMES   IN  A  MAGNETIC  FIELD  117 

The  curve  drawn  is  that  given  by  the  equation — 

100*5=3-1  X  10-7H2  +  r5  x  10-3H 
K 

where  R  denotes  the  resistance  and  H  the  magnetic  field.  It 
appears,  therefore,  that  the  effect  of  the  magnetic  field  is  made 
up  of  two  parts,  one  proportional  to  the  square  of  the  field,  and 
the  other  proportional  to  the  field.  The  lack  of  symmetry  is 
evidently  connected  with  the  upward  motion  of  the  flame. 

We  have  seen  that  when  the  top  and  bottom  of  the  flame 
are  insulated  the  horizontal  velocity  of  the  negative  ions  is 
given  by  u  =  kz  (X  —  HV),  so  that  the  conductivity  is  given  by 

v  =  nekz(l ^),  where  C  denotes  the  current. 

A.  \  A.  / 

In  the  absence  of  a  magnetic  field  the  current  C0  is  given  by 

C0  =  nekzXQ. 

Putting  a0  =  C0/X0,  a  =  C/X,  kz  —  kz  =  dkz,  and  a  —  a0  =  do, 
we  obtain,  approximately, 

do    =  d\  __  HY 

0  ~~=  kz  "     X 

eh 
We  have  kz  =  1'4— -a,*o  that  to  get  the  change  in  kz  it  is 

mil 

necessary  to  calculate  the  change  in  A,  the  mean  free  path,  due  to 
the  magnetic  field.  Consider  a  particular  free  path  making  an 
angle  6  with  H.  There  are  three  forces  acting  on  the  electron — 

(1)  Xe 

(2)  Ye  =  -  e&2H(X  -  HV) 

(3)  ReU  sin  6. 

The  electric  force  X  was  about  10  volts  per  cm.,  or  109, 
/£2HX  was  therefore  about  108,  while  HU  is  about  1010,  since 
IT  =  3  x  107.  Consequently,  the  force  Ye  can  be  neglected,  so 
that  the  effect  of  the  magnetic  field  is  due  to  the  force  HeU  sin  6. 

This  force  causes  the  electron  to  describe  an  arc  of  a  circle  of 
radius  Q  given  by 

mil*  TT  TT    •     /a 
-  HeU  sin  6. 

Q 

If  /  is  the  length  of  the  straight  line  between  the  ends  of  the 
free  path,  and  I'  the  length  along  the  arc,  we  have,  therefore, 

1  =  2e  sin  ( 


118       ELECTRICAL   PROPERTIES   OF  FLAMES 

Hence,  since  =-  is  small, 
Q 


24m2U2 
The  mean  value  of  sin2  6  is  f ,  that  of  /2  is  2A2,  and  that  of  IT'2 

H2e2/l2 
is  3U~2,  so  that  the  mean  value  of  (lf  —  1) /I'  is  equal  to  £-1^-- 

m2U2 
Hence,  since  -  ^=-  =  k 22, 

-^  =  -  TV  H  V 

for  the  time  of  describing  the  free  paths  is  increased  in  the  ratio 
of  /'  to  I. 

Sir  J.  J.  Thomson,  who  first  calculated  the  effect  of  a  magnetic 
field  on  conductivity,  on  the  electron  theory,  got  JH2&22,  but  he 
did  not  take  into  account  the  variations  of  A  and  U. 

The  equation  which  was  found  to  represent  the  experimental 
results  was — 

^5  =  3-1  x  10~9H2  +  1-5  X  10-5  H. 

If  we  assume  that  the  term  in  H2  is  equal  to  TVH2&22  we  get 
A«2  =  1-8  x  10~4  or  &2  =  18,000  for  one  volt  per  cm.  This  agrees 
as  well  as  could  be  expected  with  the  theoretical  value  of  7^2  for 

an  electron. 

y 

The  term  in  H  gives  v  =  To  X  10  ~5,  so  that  since  X  was  about 
A. 

109,  V  =  1'5  X  104,  which  is  about  one  hundred  times  too  large. 
It  is  clear,  therefore,  that  the  part  of  the  effect  proportional  to  H 
is  much  greater  than  that  to  be  expected  theoretically.  The 
reason  for  this  discrepancy  is  not  known,  and  further  experiments 
are  desirable  to  elucidate  it. 

It  was  found  that  when  the  electrodes  at  each  end  of  the 
flame  were  remo\7ed,  then  the  exploring  wires  took  up  a  potential 
difference  proportional  to  the  magnetic  field,  and  about  equal  to 
200Hrf,  where  d  is  their  distance  apart.  This  indicates  that  the 
induced  E.M.F.  in  the  flame  due  to  its  upward  motion  has  nearly 
the  value  VH  per  cm.,  as  was  to  be  expected. 


NAME   INDEX 


ARRHENIUS,  3,  75,  76,  90,  97 

Beattie,  56 
Brown,  11,  12,  48 

Cooke,  32 

Davisson,  54,  99 
Dawson,  3,  75,  76,  87,  90 
Deininger,  15 

Elster,  1 

Garrett,  53,  56 

Geitel,  1 

Giese,  2 

Gold,  62,  74,  88,  100,  109,  110 

Horton,  15,  30,  53,  54 

Hulbirt,  48 

Jeans,  90 
Jentzsch,  29,  31 

Langevin,  90,  99 
Lenard,  86 
Lusby,  84,  89 


Martyn,  20,  30 

Marx,  60,  68,  79,  85,  114,  115 

McClelland,  2 

Moreau,  84,  88 

Owen,  5,  28,  55 

Parker,  28 
Pring,  £8 

Richardson,  2,  6,  7,  11,  12,  13,  20, 
21,  26,  28,  31,  32,  38,  44,  47,  48, 
50,  51,  52,  54,  98 

Rutherford,  2,  42,  43,  44 

Smithells,  3,  75,  76,  87,  90 

Thomson,  J.  J.,  1,  2,  3,  5,  28,  30, 
40,  41,  45,  46,  53,  54,  63,  67,  79, 
90,  118 

Tufts,  69,  71 

Townsend,  16 

Wehnelt,  6,  28,  30,  31 
Wellisch,  90 
Willows,  56 
Wilson,  W.,  45 


PRINTED  FOR  THE   UNIVERSITY  OF  LONDON   PRESS.   LTD.,   BY 
RICHARD    CLAY    &    SONS,    LIMITED, 
LONDON  AND  BUNGAY. 


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